├── .gitignore
├── README.md
├── code_in_notes
    ├── Benford.do
    ├── CI_large_sample.do
    ├── CI_small_sample.do
    ├── GMM_Poisson.do
    ├── GMM_ettobit.do
    ├── GMM_mini_chi2.do
    ├── MCMC_independent_integ.py
    ├── MCMC_independent_mh.py
    ├── MCMC_logistic.py
    ├── MCMC_random_walk.py
    ├── MLE_beta.do
    ├── MLE_beta_nod.do
    ├── MLE_censor.do
    ├── MLE_liml.do
    ├── MM_beta.do
    ├── MonteCarlo_simple.py
    ├── RUN_ALL.do
    ├── Titanic.do
    ├── ab_test.do
    ├── bootstrap_lognormal.do
    ├── bootstrap_lognormal_np.do
    ├── bootstrap_student.do
    ├── box_plot.do
    ├── brownian.py
    ├── bubble_chart.do
    ├── charts_bar.do
    ├── check_random.do
    ├── check_random.py
    ├── clustering_wholesale.do
    ├── datasets
    │   ├── OHIE_ED_visit.csv
    │   ├── OHIE_QJE.dta
    │   ├── Questionarie.pdf
    │   ├── ba_sales_data.csv
    │   ├── bond_interest.xlsx
    │   ├── ccapm.dta
    │   ├── cfps_adult.dta
    │   ├── cfps_family_econ.dta
    │   ├── chfs_ind.dta
    │   ├── citydata.dta
    │   ├── export.dta
    │   ├── hs300index.dta
    │   ├── rr000005.dta
    │   ├── soep_female_labor.dta
    │   ├── titanic.dta
    │   └── wholesale.csv
    ├── descriptive_mode.do
    ├── dgp_mle_censor.ado
    ├── dgp_mle_censor_simulate.do
    ├── empirical_distribution.do
    ├── exponential.do
    ├── exponential.py
    ├── gaussian_mixture.do
    ├── gencatutility.ado
    ├── geometric_mean.do
    ├── ginindex.do
    ├── histogram_kdensity.do
    ├── importance_sampling.py
    ├── qqplot_hs300.do
    ├── rejection.py
    ├── rejection_beta.do
    ├── rejection_beta.py
    ├── rejection_trunc.do
    ├── rejection_trunc_optimal.do
    ├── scatter_weight_height.do
    ├── simulate_CLT.do
    ├── simulate_CLT.py
    ├── simulate_LLN.do
    ├── simulate_LLN.py
    ├── simulation_lm_ols_test.do
    ├── simulation_lm_test.do
    ├── simulation_lr_test.do
    ├── simulation_wald_test.do
    ├── st_call_py_tree.do
    ├── standard_normal_mean.do
    ├── standard_normal_var.do
    ├── statistic_mean.do
    ├── test_power_function.do
    ├── test_under_null.do
    ├── ttest_mean_comparison.do
    ├── twosls_by_hand.do
    ├── uniform.c
    ├── uniform.do
    ├── uniform.py
    └── zipf_law.do
├── notebook_julia
    └── Julia.ipynb
└── notebook_python
    ├── Bayes.ipynb
    ├── Brownian.ipynb
    ├── DiscreteMarkov.ipynb
    ├── LLN_CLT.ipynb
    ├── Martingale.ipynb
    ├── MonteCarlo.ipynb
    ├── Normal.ipynb
    ├── Numpy+Matplotlib+random.ipynb
    ├── Poisson_Process.ipynb
    ├── Random_number.ipynb
    ├── SDE.ipynb
    ├── Stochastic_integral.ipynb
    ├── Testing.ipynb
    ├── estimation.ipynb
    └── rejection_beta.pdf


/.gitignore:
--------------------------------------------------------------------------------
 1 | *.out
 2 | .DS_Store
 3 | *.eps
 4 | *.pdf
 5 | *.tex
 6 | *.txt
 7 | *.gph
 8 | *.ipynb_*
 9 | *.stswp
10 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | # 《数理统计》、《随机过程》课程代码
 2 | 该项目中主要包含上海对外经贸大学司继春《数理统计》课程以及《随机过程》的相关代码，主要包括讲义中的示意性代码以及Python、Julia语言的Jupyter Notebook。
 3 | ## 讲义中代码
 4 | 讲义中的代码主要包含在以下地址中：[Code in Notes](https://github.com/sijichun/MathStatsCode/tree/master/code_in_notes)，其中Stata数据文件包含在以下地址中：[Datasets](https://github.com/sijichun/MathStatsCode/tree/master/code_in_notes/datasets)。
 5 | ## Python Notebook
 6 | 除讲义中的代码以外，本课程还提供一些Jupyter Notebook。这些Notebooks可以作为编程作业的参考：
 7 | ### 《数理统计》代码
 8 | * [Numpy+Matplotlib+random 介绍](https://github.com/sijichun/MathStatsCode/blob/master/notebook_python/Numpy%2BMatplotlib%2Brandom.ipynb)
 9 | * [生成多元正态分布](https://github.com/sijichun/MathStatsCode/blob/master/notebook_python/Normal.ipynb)
10 | * [大数定律与中心极限定律](https://github.com/sijichun/MathStatsCode/blob/master/notebook_python/LLN_CLT.ipynb)
11 | * [矩估计、极大似然估计与区间估计](https://github.com/sijichun/MathStatsCode/blob/master/notebook_python/estimation.ipynb)
12 | * [假设检验](https://github.com/sijichun/MathStatsCode/blob/master/notebook_python/Testing.ipynb)
13 | ### 《随机过程》代码
14 | 
15 | * [马尔可夫链](https://github.com/sijichun/MathStatsCode/blob/master/notebook_python/DiscreteMarkov.ipynb)
16 | * [泊松过程](https://github.com/sijichun/MathStatsCode/blob/master/notebook_python/Poisson_Process.ipynb)
17 | * [布朗运动](https://github.com/sijichun/MathStatsCode/blob/master/notebook_python/Brownian.ipynb)
18 | * [蒙特卡洛](https://github.com/sijichun/MathStatsCode/blob/master/notebook_python/MonteCarlo.ipynb)
19 | ## Julia Notebook
20 | * [Julia介绍](https://github.com/sijichun/MathStatsCode/blob/master/notebook_julia/Julia.ipynb)
21 | 


--------------------------------------------------------------------------------
/code_in_notes/Benford.do:
--------------------------------------------------------------------------------
 1 | // Benford.do
 2 | clear all
 3 | use datasets/citydata.dta
 4 | keep if Year==2011
 5 | 
 6 | // 将GDP转为字符串
 7 | tostring v84, gen(gdp_string)
 8 | // 取出GDP数字字符串的第一位
 9 | gen first_digit=substr(gdp_string, 1,1)
10 | // 将第一位数字字符串转化为数字
11 | destring first_digit, replace
12 | // 统计频数
13 | tab first_digit
14 | // 创建一个数据框用于检验
15 | frame create chi2test Ng Ng_star
16 | quietly: su first_digit
17 | local N=r(N)
18 | forvalues i=1/9{
19 | 	quietly: su first_digit if first_digit==`i'
20 | 	local Ng=r(N)
21 | 	local Ng_star=`N'*(log10(`i'+1)-log10(`i'))
22 | 	frame post chi2test (`Ng') (`Ng_star')
23 | }
24 | frame chi2test: gen test_stat=(Ng-Ng_star)^2/Ng_star
25 | frame chi2test: su test_stat
26 | frame chi2test: local test_stat=r(sum)
27 | di "test statistics= `test_stat'"
28 | local p=1-chi2(8 ,`test_stat')
29 | di "p-value= `p'" 
30 | 


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/code_in_notes/CI_large_sample.do:
--------------------------------------------------------------------------------
 1 | // CI_large_sample.do
 2 | clear
 3 | set seed 97
 4 | set more off
 5 | cap program drop CIz
 6 | program define CIz, rclass
 7 | 	syntax [, obs(integer 100) mu(real 3) confident_level(real 0.95)]
 8 | 	quietly{
 9 | 		drop _all
10 | 		set obs `obs'
11 | 		tempvar d x 
12 | 		tempname lb ub alpha
13 | 		local `alpha'=1-`confident_level'
14 | 		gen `d'=runiform()<0.5
15 | 		gen `x'=`d'*(rnormal()+`mu')+(1-`d')*(rnormal()-`mu')
16 | 		su `x'
17 | 		local `lb'=r(mean)-invnormal(1-``alpha''/2)*r(sd)/sqrt(`obs')
18 | 		local `ub'=r(mean)+invnormal(1-``alpha''/2)*r(sd)/sqrt(`obs')
19 | 		return scalar lb=``lb''
20 | 		return scalar ub=``ub''
21 | 		return scalar include_true=(``lb''<=0 & ``ub''>=0)
22 | 	}
23 | end
24 | 
25 | simulate it=r(include_true), reps(10000): CIz, obs(10)
26 | su
27 | simulate it=r(include_true), reps(10000): CIz, obs(100)
28 | su
29 | 


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/code_in_notes/CI_small_sample.do:
--------------------------------------------------------------------------------
 1 | // CI_small_sample.do
 2 | clear
 3 | set seed 97
 4 | set more off
 5 | cap program drop CIt
 6 | program define CIt, rclass
 7 | 	syntax [, obs(integer 10) mu(real 0) sigma(real 1) confident_level(real 0.95)]
 8 | 	quietly{
 9 | 		drop _all
10 | 		set obs `obs'
11 | 		tempvar x 
12 | 		tempname lb ub df alpha
13 | 		local `alpha'=1-`confident_level'
14 | 		local `df'=`obs'-1
15 | 		gen `x'=`sigma'*rnormal()+`mu'
16 | 		su `x'
17 | 		local `lb'=r(mean)-invttail(``df'',``alpha''/2)*r(sd)/sqrt(`obs')
18 | 		local `ub'=r(mean)+invttail(``df'',``alpha''/2)*r(sd)/sqrt(`obs')
19 | 		return scalar lb=``lb''
20 | 		return scalar ub=``ub''
21 | 		return scalar include_true=(``lb''<=`mu' & ``ub''>=`mu')
22 | 	}
23 | end
24 | 
25 | simulate it=r(include_true), reps(10000): CIt, obs(10) mu(5) sigma(10)
26 | su


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/code_in_notes/GMM_Poisson.do:
--------------------------------------------------------------------------------
 1 | // GMM_Poisson.do
 2 | clear all
 3 | set more off
 4 | set seed 20231130
 5 | cap program drop est_lambda
 6 | program est_lambda, eclass
 7 | 	syntax varlist(max=1) [, lambda(real 1)]
 8 | 	tempvar x2
 9 | 	quietly{
10 | 		gen `x2'=`varlist'^2
11 | 		gmm (`varlist'-{lambda=`lambda'}) (`x2'-({lambda}+{lambda}^2)), winit(identity) onestep
12 | 	}
13 | 	mat b=e(b)
14 | 	mat V=e(V)
15 | 	ereturn post b V
16 | 	ereturn display
17 | end
18 | 
19 | frame create simulation lambda xmean
20 | forvalues i=1/1000{
21 | 	clear
22 | 	quietly{
23 | 		set obs 100
24 | 		gen x=rpoisson(10)
25 | 		su x
26 | 		local mean_x = r(mean)
27 | 		est_lambda x
28 | 		frame post simulation (_b[/lambda]) (`mean_x')
29 | 	}
30 | }
31 | frame simulation: su
32 | 


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/code_in_notes/GMM_ettobit.do:
--------------------------------------------------------------------------------
 1 | // GMM_ettobit.do
 2 | clear
 3 | set more off
 4 | set obs 500
 5 | set seed 8997
 6 | // 生成数据
 7 | gen x=rnormal(3,2)
 8 | local a=10
 9 | local alpha=5
10 | local beta=3
11 | local sigma=2
12 | gen y = exp(`alpha'+`beta'*x+rnormal()*sqrt(`sigma'))-`a'
13 | // 生成工具
14 | gen x2=x^2
15 | gen x3=x^3
16 | gen x_e=exp(x)
17 | gen x_sin=sin(x)
18 | // 计算a的初始值
19 | su y
20 | local a_init=-1*r(min)+5
21 | // GMM估计
22 | gmm (log({a=`a_init'}+y)-{alpha=0}-{beta=0}*x) ((log({a}+y)-{alpha}-{beta}*x)*x) ((log({a}+y)-{alpha}-{beta}*x)*x2) ((log({a}+y)-{alpha}-{beta}*x)*x3) ((log({a}+y)-{alpha}-{beta}*x)*x_e) ((log({a}+y)-{alpha}-{beta}*x)*x_sin), winit(identity)
23 | 
24 | 


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/code_in_notes/GMM_mini_chi2.do:
--------------------------------------------------------------------------------
 1 | // GMM_mini_chi2.do
 2 | clear all
 3 | set more off
 4 | set seed 20231213
 5 | cap program drop est_lambda_chi2
 6 | program est_lambda_chi2, rclass
 7 | 	syntax varname [, lambda(real 1) lambda0(real 10) n(integer 100)]
 8 | 	tempvar x2 m1_0 m2_0
 9 | 	tempname mean_m1_0 mean_m2_0 vec_g chi2_est chi2_true wmatrix objf
10 | 	quietly{
11 | 		gen `x2'=`varlist'^2
12 | 		gmm (`varlist'-{lambda=`lambda'}) (`x2'-({lambda}+{lambda}^2)), winit(identity)
13 | 		local `chi2_est'=e(J)
14 | 		mat `wmatrix'=e(W)
15 | 		gen `m1_0'=`varlist'-`lambda0'
16 | 		gen `m2_0'=`x2'-(`lambda0'+`lambda0'^2)
17 | 		su `m1_0'
18 | 		local `mean_m1_0'=r(sum)
19 | 		su `m2_0'
20 | 		local `mean_m2_0'=r(sum)
21 | 		mat `vec_g'=(``mean_m1_0'' \ ``mean_m2_0'')
22 | 		mat `objf'=`vec_g''*`wmatrix'*`vec_g'
23 | 		local `chi2_true'=`objf'[1,1]/`n'
24 | 	}
25 | 	return scalar chi2_est = ``chi2_est''
26 | 	return scalar chi2_true = ``chi2_true''
27 | end
28 | 
29 | frame create simulation chi2_est chi2_true
30 | forvalues i=1/2000{
31 | 	quietly{
32 | 		clear
33 | 		set obs 100
34 | 		gen x=rpoisson(10)
35 | 		est_lambda_chi2 x, lambda0(10) n(100)
36 | 		frame post simulation (r(chi2_est)) (r(chi2_true))
37 | 	}
38 | }
39 | frame change simulation
40 | label variable chi2_est "估计值处的目标函数"
41 | label variable chi2_true "真值处的目标函数"
42 | gen density_chi2_1=chi2den(1,chi2_est)
43 | label variable density_chi2_1 "Chi(1)密度函数"
44 | gen density_chi2_2=chi2den(2,chi2_est)
45 | label variable density_chi2_2 "Chi(2)密度函数"
46 | sort chi2_est
47 | twoway  (hist chi2_est, density) (line density_chi2_1 chi2_est  if chi2_est>0.3) (line density_chi2_2 chi2_est  if chi2_est>0.3), legend(pos(1) ring(0) label(1 "估计值处的目标函数密度")) xtitle("")
48 | graph export GMM_mini_chi2_1.pdf, replace
49 | twoway  (hist chi2_true, density) (line density_chi2_1 chi2_est  if chi2_est>0.3) (line density_chi2_2 chi2_est  if chi2_est>0.3), legend(pos(1) ring(0) label(1 "真值处的目标函数密度")) xtitle("")
50 | graph export GMM_mini_chi2_2.pdf, replace


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/code_in_notes/MCMC_independent_integ.py:
--------------------------------------------------------------------------------
 1 | ## MCMC_independent_integ.py
 2 | 
 3 | import numpy as np
 4 | from numpy import random as nprd
 5 | nprd.seed(19880505)
 6 | 
 7 | ##设定参数
 8 | M = 10000
 9 | h1 = lambda x: 0.5 * np.exp(-90 * (x[0] - 0.5)**2 - 45 * (x[1] + 0.1)**2)
10 | 
11 | ##抽样
12 | x = [(nprd.random() * 2 - 1, nprd.random() * 2 - 1) for i in range(M)]
13 | 
14 | ##计算h(x)
15 | sample = list(map(h, x))
16 | integral = 4 * np.mean(sample)
17 | se = 4 * np.std(sample) / np.sqrt(M)
18 | subsample_001 = list(filter(lambda x: x > 0.01, sample))
19 | print("Intgral=", integral)
20 | print("s.e. of Integral=", se)
21 | print("95% C.I.:", integral - 1.96 * se, "~", integral + 1.96 * se)
22 | print("Ratio of >0.01 samples:", len(subsample_001) / M)
23 | 


--------------------------------------------------------------------------------
/code_in_notes/MCMC_independent_mh.py:
--------------------------------------------------------------------------------
 1 | ## mcmc_independent_mh.py
 2 | ##独立的MCMC算法，输入：
 3 | ##    N_samples  : 抽样次数
 4 | ##      pai(x)   : 目标密度函数
 5 | ##      q(y)     : 工具密度函数
 6 | ##   q_sampler   : 给定x，从q中抽样的函数
 7 | ##      x0       : 初始值
 8 | from numpy import random as nprd
 9 | def MH_independent(N_samples, pai, q, q_sampler, x0):
10 |     X = []
11 |     x = x0
12 |     for i in range(N_samples):
13 |         y = q_sampler()
14 |         rho = min(1, pai(y) * q(x) / (pai(x) * q(y)))
15 |         if nprd.uniform() <= rho:
16 |             X.append(y)
17 |             x = y
18 |         else:
19 |             X.append(x)
20 |     return X
21 | 


--------------------------------------------------------------------------------
/code_in_notes/MCMC_logistic.py:
--------------------------------------------------------------------------------
 1 | #!/usr/bin/python3
 2 | ## file: MonteCarlo.py
 3 | 
 4 | import numpy as np
 5 | from numpy import random as nprd
 6 | 
 7 | ##设定参数
 8 | M =20000
 9 | #真值
10 | beta_0=1
11 | beta_1=1
12 | beta_2=-1
13 | #样本量
14 | N=200
15 | #Logistic函数
16 | Logistic=lambda x: 1.0/(1+np.exp(-1*x))
17 | 
18 | ##产生数据
19 | def gen_logit(N):
20 |     Data=[]
21 |     for n in range(N):
22 |         x1=nprd.normal()*1.414+1
23 |         x2=nprd.chisquare(2)
24 |         d_star=beta_0+beta_1*x1+beta_2*x2
25 |         p_star=Logistic(d_star)
26 |         d=(1 if nprd.uniform()<p_star else 0)
27 |         Data.append((d,x1,x2))
28 |     return Data
29 | 
30 | #计算接受率
31 | def rho(beta_x,beta_y,Data):
32 |     log_post_pai_x=(-1*beta_x[0]**2-beta_x[1]**2-beta_x[2]**2)/2
33 |     log_post_pai_y=(-1*beta_y[0]**2-beta_y[1]**2-beta_y[2]**2)/2
34 |     log_ratio=log_post_pai_y-log_post_pai_x
35 |     for data in Data:
36 |         w_b_x=beta_x[0]+data[1]*beta_x[1]+data[2]*beta_x[2]
37 |         w_b_y=beta_y[0]+data[1]*beta_y[1]+data[2]*beta_y[2]
38 |         F_b_x=Logistic(w_b_x)
39 |         F_b_y=Logistic(w_b_y)
40 |         log_post_pai_x=np.log((F_b_x if data[0]==1 else 1-F_b_x))
41 |         log_post_pai_y=np.log((F_b_y if data[0]==1 else 1-F_b_y))
42 |         log_ratio+=(log_post_pai_y-log_post_pai_x)
43 |     return min(1,np.exp(log_ratio))
44 | 
45 | #随机游走
46 | def q_sampler(beta):
47 |     return [b+nprd.normal(0,0.1) for b in beta]
48 | 
49 | ##独立的MCMC算法，输入：
50 | ##    N_samples  : 抽样次数
51 | ##      rho(x,y,Data)   : 计算接受率
52 | ##   q_sampler(x): 给定x，从q中抽样的函数
53 | ##      x0       : 初始值
54 | ##     data      : 数据
55 | def MH_RW(N_samples, rho, q_sampler, x0, data):
56 |     X=[]
57 |     x=x0
58 |     for i in range(N_samples):
59 |         y=q_sampler(x)
60 |         if nprd.uniform()<=rho(x,y,data):
61 |             X.append(y)
62 |             x=y
63 |         else:
64 |             X.append(x)
65 |     return X
66 | 
67 | ## 从后验抽样：
68 | data=gen_logit(N)
69 | beta_post=MH_RW(M, rho, q_sampler, [0,0,0], data)
70 | beta0_post=[b[0] for b in beta_post]
71 | sub_beta0=beta0_post[int(M*0.2):]
72 | beta1_post=[b[1] for b in beta_post]
73 | sub_beta1=beta1_post[int(M*0.2):]
74 | beta2_post=[b[2] for b in beta_post]
75 | sub_beta2=beta2_post[int(M*0.2):]
76 | #后验均值
77 | mean_beta0=np.mean(sub_beta0)
78 | mean_beta1=np.mean(sub_beta1)
79 | mean_beta2=np.mean(sub_beta2)
80 | print("Mean beta0=",mean_beta0)
81 | print("Mean beta1=",mean_beta1)
82 | print("Mean beta2=",mean_beta2)
83 | 


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/code_in_notes/MCMC_random_walk.py:
--------------------------------------------------------------------------------
 1 | #!/usr/bin/python3
 2 | ## file: MonteCarlo.py
 3 | 
 4 | import numpy as np
 5 | from numpy import random as nprd
 6 | 
 7 | ##设定参数
 8 | M =10000
 9 | pai=lambda x: np.exp(-90*(x[0]-0.5)**2-45*(x[1]+0.1)**2)
10 | domain=lambda x:(x[0]>=-1)*(x[1]>=-1)*(x[0]<=1)*(x[1]<=1)
11 | h=lambda x: domain(x)
12 | h2=lambda x: np.sin(10*x[0])**2+np.log(abs(1+x[1]*10))
13 | #从均匀分布中采样
14 | def sample_q(x):
15 |     return (x[0]+0.2*nprd.normal(),x[1]+0.2*nprd.normal())
16 | 
17 | 
18 | ##独立的MCMC算法，输入：
19 | ##    N_samples  : 抽样次数
20 | ##      pai(x)   : 目标密度函数
21 | ##   q_sampler(x): 给定x，从q中抽样的函数
22 | ##      x0       : 初始值
23 | def MH_RW(N_samples, pai, q_sampler, x0):
24 |     X=[]
25 |     x=x0
26 |     for i in range(N_samples):
27 |         y=q_sampler(x)
28 |         rho=min(1,pai(y)/pai(x))
29 |         if nprd.uniform()<rho:
30 |             X.append(y)
31 |             x=y
32 |         else:
33 |             X.append(x)
34 |     return X
35 | 
36 | ## 计算积分
37 | x=MH_RW(M, pai, sample_q, (0,0))
38 | ## 第一个积分
39 | H=list(map(h,x))
40 | ## 取h后面80%的样本
41 | subH=H[int(M*0.2):]
42 | integral=np.pi/(90*np.sqrt(2))*np.mean(subH)
43 | print("Intgral1=",integral)
44 | ## 第二个积分
45 | H2=list(map(h2,x))
46 | subH2=H2[int(M*0.2):]
47 | integral2=np.pi/(90*np.sqrt(2))*np.mean(subH2)
48 | print("Intgral2=",integral2)
49 | 
50 | 


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/code_in_notes/MLE_beta.do:
--------------------------------------------------------------------------------
 1 | // MLE_beta.do
 2 | clear
 3 | set seed 8855
 4 | // 目标函数 
 5 | cap program drop betaobj 
 6 | program betaobj 	
 7 | 	args todo b lnfj g1 g2
 8 | 	tempvar alpha beta lnx ln1x
 9 | 	mleval `alpha'=`b', eq(1)
10 | 	mleval `beta'=`b', eq(2)
11 | 	quietly{
12 | 		gen `lnx'=log($ML_y1)
13 | 		gen `ln1x'=log(1-$ML_y1)
14 | 		replace `lnfj'=lngamma(`alpha'+`beta')-lngamma(`alpha')-lngamma(`beta')+(`alpha'-1)*`lnx'+(`beta'-1)*`ln1x'
15 | 		if (`todo'==0) exit  //如果不需要计算导数，退出
16 | 		replace `g1'=digamma(`alpha'+`beta')-digamma(`alpha')+`lnx'
17 | 		replace `g2'=digamma(`alpha'+`beta')-digamma(`beta')+`ln1x'
18 | 	} 
19 | end 
20 | set obs 1000 
21 | gen x=rbeta(0.5,3)
22 | ml model lf1 betaobj (alpha: x = , freeparm) /beta
23 | ml search 
24 | ml maximize
25 | 


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/code_in_notes/MLE_beta_nod.do:
--------------------------------------------------------------------------------
 1 | // MLE_beta_nod.do
 2 | clear
 3 | set seed 8855
 4 | // 目标函数 
 5 | cap program drop betaobj 
 6 | program betaobj 	
 7 | 	args lnfj theta1 theta2
 8 | 	quietly{ 		
 9 | 		replace `lnfj'=log(betaden(`theta1',`theta2',x))
10 | 	} 
11 | end 
12 | // 产生Beta分布数据
13 | set obs 1000 
14 | gen x=rbeta(0.5,3)
15 | // 定义极大似然问题 
16 | ml model lf betaobj /alpha /beta 
17 | // 寻找初始点（可选）
18 | ml search 
19 | // 最大化 并得到结果
20 | ml maximize
21 | 


--------------------------------------------------------------------------------
/code_in_notes/MLE_censor.do:
--------------------------------------------------------------------------------
 1 | // MLE_censor.do
 2 | clear
 3 | // 定义目标函数
 4 | cap program drop ml_censor_obj
 5 | program ml_censor_obj
 6 | 	args lnfj theta1 theta2
 7 | 	tempvar lnx
 8 | 	quietly{
 9 | 		gen `lnx'=log10($ML_y1)
10 | 		replace `lnfj'=lnnormalden((`lnx'-`theta1')/sqrt(`theta2'))-log(sqrt(`theta2')) if `lnx'>3 & `lnx'<4
11 | 		replace `lnfj'=lnnormal((3-`theta1')/sqrt(`theta2')) if `lnx'==3
12 | 		replace `lnfj'=log(1-normal((4-`theta1')/sqrt(`theta2'))) if `lnx'==4
13 | 	}
14 | end
15 | // 进行极大似然估计
16 | cap program drop mle_censor
17 | program mle_censor, eclass
18 | 	syntax varlist(max=1)
19 | 	quietly{
20 | 		ml model lf ml_censor_obj (mu: `varlist'=, freeparm) /sigma2
21 | 		ml search
22 | 		noisily: ml maximize
23 | 		mat b=e(b)
24 | 		mat V=e(V)
25 | 		ereturn post b V
26 | 	}
27 | end
28 | 
29 | set seed 8855
30 | dgp_mle_censor x, obs(500) mu(3.3) sigma2(1)
31 | mle_censor x
32 | 


--------------------------------------------------------------------------------
/code_in_notes/MLE_liml.do:
--------------------------------------------------------------------------------
 1 | clear
 2 | set more off
 3 | 
 4 | // LIML by hand
 5 | cap program drop limlobj
 6 | program limlobj
 7 | 	args todo b lnfj g1 g2 g3
 8 | 	tempvar theta1 theta2 theta3 resid2 resid1
 9 | 	tempname sigma1 sigma2
10 | 	mleval `theta1'=`b', eq(1)
11 | 	mleval `theta2'=`b', eq(2)
12 | 	mleval `theta3'=`b', eq(3)
13 | 	quietly{
14 | 		gen `resid1'=.
15 | 		gen `resid2'=.
16 | 		replace `resid2'=$ML_y2 - `theta2'
17 | 		replace `resid1'=$ML_y1 - `theta1' - `theta3'*`resid2'
18 | 		su `resid1'
19 | 		scalar `sigma1'=r(sd)
20 | 		su `resid2'
21 | 		scalar `sigma2'=r(sd)
22 | 		replace `lnfj'=-log(`sigma1')-log(`sigma2') /*
23 | 			*/-`resid1'^2/(`sigma1'^2*2) /*
24 | 			*/-`resid2'^2/(`sigma2'^2*2)
25 | 		if (`todo'==0) exit
26 | 		replace `g1'=1/(`sigma1'^2)*`resid1'
27 | 		replace `g2'=-1/(`sigma1'^2)*`resid1'*`theta3'/*
28 | 			*/+1/(`sigma2'^2)*`resid2'
29 | 		replace `g3'=1/(`sigma1'^2)*`resid1'*`resid2'	
30 | 	}
31 | end
32 | 
33 | cap program drop liml
34 | program liml, eclass
35 | 	version 15.0
36 | 	// endo: 内生变量，至多一个
37 | 	// instru: 工具变量，control：控制变量
38 | 	// endofunc: 内生变量的函数
39 | 	syntax varlist(max=1), endo(varlist max=1) /*
40 | 		*/ instru(varlist) control(varlist) [endofc(varlist)]
41 | 	tempname dep x z b0 b1 initb
42 | 	local `dep' "`varlist'"
43 | 	local `x' "`endo' `endofc' `control'"
44 | 	local `z' "`instru' `control'"
45 | 	ml model lf1 limlobj (Structual:``dep'' = ``x'') /*
46 | 		*/ (First_stage:`endo' = ``z'') /rho
47 | 	quietly{ //使用最小二乘估计作为初始值
48 | 		reg ``dep'' ``x''
49 | 		mat `b0'=e(b)
50 | 		reg `endo' ``z''
51 | 		mat `b1'=e(b)
52 | 		mat `initb'=(`b0', `b1', 0)
53 | 		ml init `initb', copy
54 | 	}
55 | 	ml maximize
56 | end
57 | 
58 | set obs 1000
59 | // generate data
60 | gen z=rnormal()
61 | gen u=rnormal()
62 | gen x1=z+rnormal()+u
63 | gen x2=z+0.5*rnormal()
64 | gen y=x1+x2+u
65 | // 官方LIML
66 | ivregress liml  y (x1=z) x2 // 最简单情况，与2SLS等价
67 | // 手写LIML
68 | liml y, endo(x1) instru(z) control(x2)
69 | 


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/code_in_notes/MM_beta.do:
--------------------------------------------------------------------------------
 1 | // MM_beta.do
 2 | clear all
 3 | set more off
 4 | set seed 20221130
 5 | cap program drop est_beta
 6 | program est_beta, eclass
 7 | 	syntax varlist(max=1) [, alpha(real 1) beta(real 1)]
 8 | 	tempvar x2
 9 | 	quietly{
10 | 		gen `x2'=`varlist'^2
11 | 		gmm (`varlist'-({alpha=`alpha'}/({alpha}+{beta=`beta'}))) (`x2'-({alpha}*{beta}+{alpha}^2*({alpha}+{beta}+1))/(({alpha}+{beta})^2*({alpha}+{beta}+1))), winit(identity)
12 | 	}
13 | 	mat b=e(b)
14 | 	mat V=e(V)
15 | 	ereturn post b V
16 | 	ereturn display
17 | end
18 | 
19 | frame create simulation alpha beta
20 | forvalues i=1/1000{
21 | 	clear
22 | 	quietly{
23 | 		set obs 100
24 | 		gen x=rbeta(1.2,0.5)
25 | 		est_beta x
26 | 		frame post simulation (_b[/alpha]) (_b[/beta])
27 | 	}
28 | }
29 | frame simulation: su


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/code_in_notes/MonteCarlo_simple.py:
--------------------------------------------------------------------------------
 1 | ## MonteCarlo_simple.py
 2 | 
 3 | import numpy as np
 4 | from numpy import random as nprd
 5 | 
 6 | ##设定参数
 7 | M = 10000
 8 | h1 = lambda x: 0.5 * np.exp(-90 * (x[0] - 0.5)**2 - 45 * (x[1] + 0.1)**2)
 9 | 
10 | ##抽样
11 | x = [(nprd.random() * 2 - 1, nprd.random() * 2 - 1) for i in range(M)]
12 | 
13 | ##计算h(x)
14 | sample = list(map(h1, x))
15 | integral = 4 * np.mean(sample)
16 | se = 4 * np.std(sample) / np.sqrt(M)
17 | subsample_001 = list(filter(lambda x: x > 0.01, sample))
18 | print("Intgral=", integral)
19 | print("s.e. of Integral=", se)
20 | print("95% C.I.:", integral - 1.96 * se, "~", integral + 1.96 * se)
21 | print("Ratio of >0.01 samples:", len(subsample_001) / M)
22 | 


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/code_in_notes/RUN_ALL.do:
--------------------------------------------------------------------------------
 1 | clear
 2 | set more off
 3 | ** begin
 4 | do uniform.do
 5 | do check_random.do
 6 | do exponential.do
 7 | do rejection_trunc.do
 8 | do rejection_trunc_optimal.do
 9 | do gaussian_mixture.do
10 | do standard_normal_var.do
11 | do standard_normal_mean.do
12 | do test_power_function.do
13 | do qqplot_hs300.do
14 | do statistic_mean.do
15 | do empirical_distribution.do
16 | do simulate_LLN.do
17 | do simulate_CLT.do
18 | do histogram_kdensity.do
19 | do charts_bar.do
20 | do scatter_weight_height.do
21 | do zipf_law.do
22 | do bubble_chart.do
23 | do box_plot.do
24 | do bootstrap_lognormal.do
25 | do test_power_function.do
26 | do simulation_wald_test.do
27 | do simulation_lm_test.do
28 | do simulation_lm_ols_test.do
29 | do simulation_lr_test.do
30 | do GMM_mini_chi2.do
31 | do dgp_mle_censor_simulate.do
32 | 


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/code_in_notes/Titanic.do:
--------------------------------------------------------------------------------
 1 | // Titanic.do
 2 | clear all
 3 | use datasets/titanic.dta
 4 | // 按照性别加总
 5 | collapse (sum)num_aboard (sum)num_death, by(sex)
 6 | // 计算幸存人数
 7 | gen num_survive=num_aboard-num_death
 8 | // 计算死亡总人数、幸存总人数
 9 | qui: sum num_death
10 | local death=r(sum)
11 | qui: sum num_survive
12 | local survive=r(sum)
13 | local N=`death'+`survive'
14 | // 计算理论死亡、幸存人数
15 | gen e_num_death=num_aboard*`death'/`N'
16 | gen e_num_survive=num_aboard*`survive'/`N'
17 | // 计算检验统计量
18 | gen chi2_death=(num_death-e_num_death)^2/e_num_death
19 | gen chi2_survive=(num_survive-e_num_survive)^2/e_num_survive
20 | gen chi2=chi2_death+chi2_survive
21 | qui: su chi2
22 | local test_stat=r(sum)
23 | di "test statistics= `test_stat'"
24 | local p=1-chi2(2 ,`test_stat')
25 | di "p-value= `p'" 
26 | 


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/code_in_notes/ab_test.do:
--------------------------------------------------------------------------------
 1 | // ab_test.do
 2 | // 导入数据
 3 | clear
 4 | set more off
 5 | import delimited "datasets/ba_sales_data.csv"
 6 | 
 7 | // 加总用户交易量
 8 | collapse (sum) sale_price (max) test_option, by(user_id)
 9 | 
10 | // 进行检验
11 | ttest sale_price, by(test_option)
12 | 


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/code_in_notes/bootstrap_lognormal.do:
--------------------------------------------------------------------------------
 1 | // bootstrap_lognormal.do
 2 | clear all
 3 | set more off
 4 | set seed 1000
 5 | set obs 10
 6 | // 产生样本
 7 | local mu=2
 8 | gen z=rnormal(`mu',sqrt(2))
 9 | gen x=exp(z)
10 | // 进行估计
11 | su x
12 | local mu_hat=log(r(mean))-1
13 | di `mu_hat'
14 | // 进行再抽样，将再抽样结果放入到数据框bootstrap中
15 | frame create bootstrap mu_star
16 | local B=10000
17 | forvalues i=1/`B'{
18 | 	quietly{
19 | 		gen z_star=rnormal(`mu_hat',sqrt(2))
20 | 		gen x_star=exp(z_star)
21 | 		su x_star
22 | 		local mu_star=log(r(mean))-1
23 | 		frame post bootstrap (`mu_star')
24 | 		drop z_star
25 | 		drop x_star
26 | 	}
27 | }
28 | frame bootstrap: hist mu_star
29 | graph export bootstrap_lognormal.pdf, replace
30 | frame bootstrap: su mu_star, de
31 | local mu_star_bar=r(mean)
32 | di "mu_bc=" _skip 2*`mu_hat'-`mu_star_bar'


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/code_in_notes/bootstrap_lognormal_np.do:
--------------------------------------------------------------------------------
 1 | // bootstrap_lognormal_np.do
 2 | clear all
 3 | set more off
 4 | set seed 1000
 5 | set obs 10
 6 | // 产生样本
 7 | local mu=2
 8 | gen z=rnormal(`mu',sqrt(2))
 9 | gen x=exp(z)
10 | // 定义估计的program
11 | cap drop program lognormalest
12 | program define lognormalest, rclass
13 | 	syntax varname
14 | 	quietly {
15 | 		su `varlist'
16 | 		local mu=log(r(mean))-1
17 | 		return scalar mu=`mu'
18 | 	}
19 | end
20 | // bootstrap
21 | local B=1000
22 | bootstrap mu=r(mu), reps(`B'): lognormalest x
23 | estat bootstrap 


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/code_in_notes/bootstrap_student.do:
--------------------------------------------------------------------------------
 1 | // bootstrap_student.do
 2 | clear all
 3 | use datasets/OHIE_QJE.dta
 4 | // bootstrap
 5 | bootstrap b=_b[treatment] se=_se[treatment], reps(200) seed(55) cluster(household_id) saving(bootstrap_student.dta, replace): reg birthyear_list treatment, vce(bootstrap)
 6 | // 进行回归，保存系数和标准误
 7 | reg birthyear_list treatment
 8 | local b=_b[treatment]
 9 | local se=_se[treatment]
10 | // 打开一个数据框，装入bootstrap_student.dta
11 | frame create bootstrap_sample
12 | frame change bootstrap_sample
13 | use bootstrap_student.dta
14 | gen t=(b-`b')/se
15 | sort t
16 | local alpha_25=(t[floor(_N*0.025)]+t[ceil(_N*0.025)])/2
17 | local alpha_975=(t[floor(_N*0.975)]+t[ceil(_N*0.975)])/2
18 | // 计算好分位数，返回
19 | frame change default
20 | rm bootstrap_student.dta
21 | // 计算置信区间
22 | di "置信区间为：" _skip "[" `b'-`alpha_975'*`se' "," `b'-`alpha_25'*`se' "]"
23 | 


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/code_in_notes/box_plot.do:
--------------------------------------------------------------------------------
1 | // box_plot.do
2 | clear
3 | use datasets/cfps_adult.dta
4 | drop if qp101<0
5 | graph box qp101, noout
6 | graph export box_plot.pdf, replace
7 | graph hbox qp101, over(cfps_gender)
8 | graph export box_plot_by_sex.pdf, replace
9 | 


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/code_in_notes/brownian.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | import numpy.random as nprd
 3 | 
 4 | t=np.linspace(0.0,5.0,5000)
 5 | B1=np.zeros(len(t))
 6 | B2=np.zeros(len(t))
 7 | B3=np.zeros(len(t))
 8 | B4=np.zeros(len(t))
 9 | B5=np.zeros(len(t))
10 | B6=np.zeros(len(t))
11 | b1=b2=b3=b4=b5=b6=0
12 | epsilon=np.sqrt(t[1]-t[0])
13 | for tt in range(len(t)):
14 |     B1[tt]=b1
15 |     b1=b1+nprd.normal(0,epsilon)
16 |     B2[tt]=b2
17 |     b2=b2+nprd.normal(0,epsilon)
18 |     B3[tt]=b3
19 |     b3=b3+nprd.normal(0,epsilon)
20 |     B4[tt]=b4
21 |     b4=b4+nprd.normal(0,epsilon)
22 |     B5[tt]=b5
23 |     b5=b5+nprd.normal(0,epsilon)
24 |     B6[tt]=b6
25 |     b6=b6+nprd.normal(0,epsilon)
26 | 
27 | import matplotlib.pyplot as plt
28 | # 设定图像大小
29 | plt.rcParams['figure.figsize'] = (10.0, 10.0)
30 | plt.figure(0)
31 | plt.plot(t,B1,label=r'Brownian Motion1',color='blue')
32 | plt.plot(t,B2,label=r'Brownian Motion2',color='red')
33 | plt.plot(t,B3,label=r'Brownian Motion3',color='pink')
34 | plt.plot(t,B4,label=r'Brownian Motion4',color='green')
35 | plt.plot(t,B5,label=r'Brownian Motion5',color='orange')
36 | plt.plot(t,B6,label=r'Brownian Motion6',color='yellow')
37 | plt.legend(loc='upper left', frameon=True)
38 | plt.savefig("brownian_motion.eps")
39 | 
40 | t=np.linspace(0.0,5.0,10000)
41 | B1=np.zeros(len(t))
42 | B2=np.zeros(len(t))
43 | B3=np.zeros(len(t))
44 | B4=np.zeros(len(t))
45 | B5=np.zeros(len(t))
46 | B6=np.zeros(len(t))
47 | b1=b2=b3=b4=b5=b6=0
48 | epsilon=np.sqrt(t[1]-t[0])
49 | for tt in range(len(t)):
50 |     B1[tt]=b1
51 |     b1=b1+nprd.normal(0,epsilon)
52 |     B2[tt]=b2
53 |     b2=b2+nprd.normal(0,epsilon)
54 |     B3[tt]=b3
55 |     b3=b3+nprd.normal(0,epsilon)
56 |     B4[tt]=b4
57 |     b4=b4+nprd.normal(0,epsilon)
58 |     B5[tt]=b5
59 |     b5=b5+nprd.normal(0,epsilon)
60 |     B6[tt]=b6
61 |     b6=b6+nprd.normal(0,epsilon)
62 | 
63 | plt.figure(1)
64 | plt.plot(B1,B2,label=r'Brownian Motion1',color='blue')
65 | plt.plot(B3,B4,label=r'Brownian Motion2',color='red')
66 | plt.plot(B5,B6,label=r'Brownian Motion3',color='green')
67 | plt.legend(loc='upper left', frameon=True)
68 | plt.savefig("brownian_motion_2d.eps")
69 | 


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/code_in_notes/bubble_chart.do:
--------------------------------------------------------------------------------
 1 | // bubble_chart.do
 2 | clear
 3 | use datasets/citydata.dta
 4 | keep if Year==2011
 5 | // 省份代码、判断东中西部
 6 | gen prov=floor(CityCode/10000)
 7 | gen east=inlist(prov,11,12,13,21,31,32,33,35,37,44,46)
 8 | gen middle=inlist(prov,14,22,23,34,36,41,43,42)
 9 | gen west=inlist(prov,15,45,50,51,52,53,54,61,62,63,64,65)
10 | // 产生变量
11 | gen log_gdp_per_capita=log(v84)-log(v86)
12 | gen log_pop=log(v86)
13 | gen log_waste_water=log(v266)
14 | // 画图
15 | twoway (scatter log_waste_water log_gdp_per_capita [fw=v86] if east, msize(tiny) mcolor(blue%30)) (scatter log_waste_water log_gdp_per_capita [fw=v86] if middle, msize(tiny) mcolor(green%30)) (scatter log_waste_water log_gdp_per_capita [fw=v86] if west, msize(tiny) mcolor(red%30)), legend(off) xtitle("对数人均GDP") ytitle("对数工业废水排放量")
16 | graph export bubble_chart.pdf, replace
17 | 


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/code_in_notes/charts_bar.do:
--------------------------------------------------------------------------------
 1 | // charts_bar.do
 2 | use datasets/cfps_adult.dta, clear
 3 | drop if te4<0
 4 | graph bar, over(te4, label(angle(15)))
 5 | graph export chart_bar1.pdf, replace
 6 | graph bar (count), over(te4, label(angle(15)))
 7 | graph export chart_bar2.pdf, replace
 8 | graph hbar (mean) p_income, over(te4)
 9 | graph export chart_bar3.pdf, replace
10 | collapse (count) p_income (mean) mean_income = p_income (median) median_income = p_income, by(te4)
11 | gen te4_left=te4-0.2
12 | gen te4_right=te4+0.2
13 | twoway (bar mean_income te4_left, barw(0.2)) (bar median_income te4, barw(0.2)) (bar p_income te4_right, yaxis(2) barw(0.2)), xlabel(1 "文盲" 2 "小学" 3 "初中" 4 "高中" 5 "大专'" 6 "本科" 7 "研究生") ytitle("金额", axis(1)) ytitle("人数", axis(2)) legend(pos(11) ring(0) label(1 "收入均值") label(2 "收入中位数") lab(3 "人数"))
14 | graph export chart_bar4.pdf, replace
15 | 


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/code_in_notes/check_random.do:
--------------------------------------------------------------------------------
 1 | // check_random.do
 2 | set more off
 3 | clear
 4 | set obs 1000
 5 | // 行号是奇数还是偶数
 6 | gen variable_id=mod(_n,2)
 7 | gen group=ceil(_n/2)
 8 | // 产生序贯的随机数
 9 | gen x=runiform()
10 | // 将奇数观测作为x1，偶数观测作为x0
11 | reshape wide x, i(group) j(variable_id)
12 | // 画散点图
13 | scatter x1 x0 ,  graphr(fcolor(white) color(white))
14 | // 保存图片
15 | graph export check_random_stata.eps, replace
16 | 


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/code_in_notes/check_random.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | import numpy.random as nprd
 3 | # 获取序贯的1000个均匀分布随机数
 4 | x = nprd.random(1000)
 5 | # 将1000个均匀分布随机数按照奇偶数分成两个序列x0 和x1
 6 | x0 = np.array([x[i] for i in range(1000) if i % 2 == 0])
 7 | x1 = np.array([x[i] for i in range(1000) if i % 2 == 1])
 8 | # 画图
 9 | import matplotlib.pyplot as plt
10 | # 设定图像大小
11 | plt.rcParams['figure.figsize'] = (8.0, 5.0)
12 | plt.scatter(x0, x1, color='blue')  ## 画出散点图
13 | plt.savefig("check_random_py.pdf")


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/code_in_notes/clustering_wholesale.do:
--------------------------------------------------------------------------------
 1 | // clustering.do
 2 | // 导入数据
 3 | clear
 4 | set more off
 5 | import delimited "datasets/wholesale.csv"
 6 | 
 7 | /* 进行聚类，使用层次聚类:
 8 | average linkage
 9 | angular（角度，余弦相似度）*/
10 | cluster averagelinkage fresh milk grocery frozen detergents_paper delicassen, measure(angular)
11 | // 画图
12 | //cluster dendrogram, cutnumber(30)
13 | // 分5类
14 | cluster gen cluster1=groups(5)
15 | // kmeans 聚类，使用层次聚类的结果作为初试类别
16 | cluster kmeans fresh milk grocery frozen, /*
17 | 	*/k(5) measure(angular) start(group(cluster1))
18 | rename _clus_2 cluster_kmeans
19 | // 画图，比如fresh和grocery
20 | twoway (scatter fresh grocery if cluster_kmeans==1)/*
21 | 	 */(scatter fresh grocery if cluster_kmeans==2)/*
22 | 	 */(scatter fresh grocery if cluster_kmeans==3)/*
23 | 	 */(scatter fresh grocery if cluster_kmeans==4)/*
24 | 	 */(scatter fresh grocery if cluster_kmeans==5), legend(off)
25 | 


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  1 | Channel,Region,Fresh,Milk,Grocery,Frozen,Detergents_Paper,Delicassen
  2 | 2,3,12669,9656,7561,214,2674,1338
  3 | 2,3,7057,9810,9568,1762,3293,1776
  4 | 2,3,6353,8808,7684,2405,3516,7844
  5 | 1,3,13265,1196,4221,6404,507,1788
  6 | 2,3,22615,5410,7198,3915,1777,5185
  7 | 2,3,9413,8259,5126,666,1795,1451
  8 | 2,3,12126,3199,6975,480,3140,545
  9 | 2,3,7579,4956,9426,1669,3321,2566
 10 | 1,3,5963,3648,6192,425,1716,750
 11 | 2,3,6006,11093,18881,1159,7425,2098
 12 | 2,3,3366,5403,12974,4400,5977,1744
 13 | 2,3,13146,1124,4523,1420,549,497
 14 | 2,3,31714,12319,11757,287,3881,2931
 15 | 2,3,21217,6208,14982,3095,6707,602
 16 | 2,3,24653,9465,12091,294,5058,2168
 17 | 1,3,10253,1114,3821,397,964,412
 18 | 2,3,1020,8816,12121,134,4508,1080
 19 | 1,3,5876,6157,2933,839,370,4478
 20 | 2,3,18601,6327,10099,2205,2767,3181
 21 | 1,3,7780,2495,9464,669,2518,501
 22 | 2,3,17546,4519,4602,1066,2259,2124
 23 | 1,3,5567,871,2010,3383,375,569
 24 | 1,3,31276,1917,4469,9408,2381,4334
 25 | 2,3,26373,36423,22019,5154,4337,16523
 26 | 2,3,22647,9776,13792,2915,4482,5778
 27 | 2,3,16165,4230,7595,201,4003,57
 28 | 1,3,9898,961,2861,3151,242,833
 29 | 1,3,14276,803,3045,485,100,518
 30 | 2,3,4113,20484,25957,1158,8604,5206
 31 | 1,3,43088,2100,2609,1200,1107,823
 32 | 1,3,18815,3610,11107,1148,2134,2963
 33 | 1,3,2612,4339,3133,2088,820,985
 34 | 1,3,21632,1318,2886,266,918,405
 35 | 1,3,29729,4786,7326,6130,361,1083
 36 | 1,3,1502,1979,2262,425,483,395
 37 | 2,3,688,5491,11091,833,4239,436
 38 | 1,3,29955,4362,5428,1729,862,4626
 39 | 2,3,15168,10556,12477,1920,6506,714
 40 | 2,3,4591,15729,16709,33,6956,433
 41 | 1,3,56159,555,902,10002,212,2916
 42 | 1,3,24025,4332,4757,9510,1145,5864
 43 | 1,3,19176,3065,5956,2033,2575,2802
 44 | 2,3,10850,7555,14961,188,6899,46
 45 | 2,3,630,11095,23998,787,9529,72
 46 | 2,3,9670,7027,10471,541,4618,65
 47 | 2,3,5181,22044,21531,1740,7353,4985
 48 | 2,3,3103,14069,21955,1668,6792,1452
 49 | 2,3,44466,54259,55571,7782,24171,6465
 50 | 2,3,11519,6152,10868,584,5121,1476
 51 | 2,3,4967,21412,28921,1798,13583,1163
 52 | 1,3,6269,1095,1980,3860,609,2162
 53 | 1,3,3347,4051,6996,239,1538,301
 54 | 2,3,40721,3916,5876,532,2587,1278
 55 | 2,3,491,10473,11532,744,5611,224
 56 | 1,3,27329,1449,1947,2436,204,1333
 57 | 1,3,5264,3683,5005,1057,2024,1130
 58 | 2,3,4098,29892,26866,2616,17740,1340
 59 | 2,3,5417,9933,10487,38,7572,1282
 60 | 1,3,13779,1970,1648,596,227,436
 61 | 1,3,6137,5360,8040,129,3084,1603
 62 | 2,3,8590,3045,7854,96,4095,225
 63 | 2,3,35942,38369,59598,3254,26701,2017
 64 | 2,3,7823,6245,6544,4154,4074,964
 65 | 2,3,9396,11601,15775,2896,7677,1295
 66 | 1,3,4760,1227,3250,3724,1247,1145
 67 | 2,3,85,20959,45828,36,24231,1423
 68 | 1,3,9,1534,7417,175,3468,27
 69 | 2,3,19913,6759,13462,1256,5141,834
 70 | 1,3,2446,7260,3993,5870,788,3095
 71 | 1,3,8352,2820,1293,779,656,144
 72 | 1,3,16705,2037,3202,10643,116,1365
 73 | 1,3,18291,1266,21042,5373,4173,14472
 74 | 1,3,4420,5139,2661,8872,1321,181
 75 | 2,3,19899,5332,8713,8132,764,648
 76 | 2,3,8190,6343,9794,1285,1901,1780
 77 | 1,3,20398,1137,3,4407,3,975
 78 | 1,3,717,3587,6532,7530,529,894
 79 | 2,3,12205,12697,28540,869,12034,1009
 80 | 1,3,10766,1175,2067,2096,301,167
 81 | 1,3,1640,3259,3655,868,1202,1653
 82 | 1,3,7005,829,3009,430,610,529
 83 | 2,3,219,9540,14403,283,7818,156
 84 | 2,3,10362,9232,11009,737,3537,2342
 85 | 1,3,20874,1563,1783,2320,550,772
 86 | 2,3,11867,3327,4814,1178,3837,120
 87 | 2,3,16117,46197,92780,1026,40827,2944
 88 | 2,3,22925,73498,32114,987,20070,903
 89 | 1,3,43265,5025,8117,6312,1579,14351
 90 | 1,3,7864,542,4042,9735,165,46
 91 | 1,3,24904,3836,5330,3443,454,3178
 92 | 1,3,11405,596,1638,3347,69,360
 93 | 1,3,12754,2762,2530,8693,627,1117
 94 | 2,3,9198,27472,32034,3232,18906,5130
 95 | 1,3,11314,3090,2062,35009,71,2698
 96 | 2,3,5626,12220,11323,206,5038,244
 97 | 1,3,3,2920,6252,440,223,709
 98 | 2,3,23,2616,8118,145,3874,217
 99 | 1,3,403,254,610,774,54,63
100 | 1,3,503,112,778,895,56,132
101 | 1,3,9658,2182,1909,5639,215,323
102 | 2,3,11594,7779,12144,3252,8035,3029
103 | 2,3,1420,10810,16267,1593,6766,1838
104 | 2,3,2932,6459,7677,2561,4573,1386
105 | 1,3,56082,3504,8906,18028,1480,2498
106 | 1,3,14100,2132,3445,1336,1491,548
107 | 1,3,15587,1014,3970,910,139,1378
108 | 2,3,1454,6337,10704,133,6830,1831
109 | 2,3,8797,10646,14886,2471,8969,1438
110 | 2,3,1531,8397,6981,247,2505,1236
111 | 2,3,1406,16729,28986,673,836,3
112 | 1,3,11818,1648,1694,2276,169,1647
113 | 2,3,12579,11114,17569,805,6457,1519
114 | 1,3,19046,2770,2469,8853,483,2708
115 | 1,3,14438,2295,1733,3220,585,1561
116 | 1,3,18044,1080,2000,2555,118,1266
117 | 1,3,11134,793,2988,2715,276,610
118 | 1,3,11173,2521,3355,1517,310,222
119 | 1,3,6990,3880,5380,1647,319,1160
120 | 1,3,20049,1891,2362,5343,411,933
121 | 1,3,8258,2344,2147,3896,266,635
122 | 1,3,17160,1200,3412,2417,174,1136
123 | 1,3,4020,3234,1498,2395,264,255
124 | 1,3,12212,201,245,1991,25,860
125 | 2,3,11170,10769,8814,2194,1976,143
126 | 1,3,36050,1642,2961,4787,500,1621
127 | 1,3,76237,3473,7102,16538,778,918
128 | 1,3,19219,1840,1658,8195,349,483
129 | 2,3,21465,7243,10685,880,2386,2749
130 | 1,3,140,8847,3823,142,1062,3
131 | 1,3,42312,926,1510,1718,410,1819
132 | 1,3,7149,2428,699,6316,395,911
133 | 1,3,2101,589,314,346,70,310
134 | 1,3,14903,2032,2479,576,955,328
135 | 1,3,9434,1042,1235,436,256,396
136 | 1,3,7388,1882,2174,720,47,537
137 | 1,3,6300,1289,2591,1170,199,326
138 | 1,3,4625,8579,7030,4575,2447,1542
139 | 1,3,3087,8080,8282,661,721,36
140 | 1,3,13537,4257,5034,155,249,3271
141 | 1,3,5387,4979,3343,825,637,929
142 | 1,3,17623,4280,7305,2279,960,2616
143 | 1,3,30379,13252,5189,321,51,1450
144 | 1,3,37036,7152,8253,2995,20,3
145 | 1,3,10405,1596,1096,8425,399,318
146 | 1,3,18827,3677,1988,118,516,201
147 | 2,3,22039,8384,34792,42,12591,4430
148 | 1,3,7769,1936,2177,926,73,520
149 | 1,3,9203,3373,2707,1286,1082,526
150 | 1,3,5924,584,542,4052,283,434
151 | 1,3,31812,1433,1651,800,113,1440
152 | 1,3,16225,1825,1765,853,170,1067
153 | 1,3,1289,3328,2022,531,255,1774
154 | 1,3,18840,1371,3135,3001,352,184
155 | 1,3,3463,9250,2368,779,302,1627
156 | 1,3,622,55,137,75,7,8
157 | 2,3,1989,10690,19460,233,11577,2153
158 | 2,3,3830,5291,14855,317,6694,3182
159 | 1,3,17773,1366,2474,3378,811,418
160 | 2,3,2861,6570,9618,930,4004,1682
161 | 2,3,355,7704,14682,398,8077,303
162 | 2,3,1725,3651,12822,824,4424,2157
163 | 1,3,12434,540,283,1092,3,2233
164 | 1,3,15177,2024,3810,2665,232,610
165 | 2,3,5531,15726,26870,2367,13726,446
166 | 2,3,5224,7603,8584,2540,3674,238
167 | 2,3,15615,12653,19858,4425,7108,2379
168 | 2,3,4822,6721,9170,993,4973,3637
169 | 1,3,2926,3195,3268,405,1680,693
170 | 1,3,5809,735,803,1393,79,429
171 | 1,3,5414,717,2155,2399,69,750
172 | 2,3,260,8675,13430,1116,7015,323
173 | 2,3,200,25862,19816,651,8773,6250
174 | 1,3,955,5479,6536,333,2840,707
175 | 2,3,514,7677,19805,937,9836,716
176 | 1,3,286,1208,5241,2515,153,1442
177 | 2,3,2343,7845,11874,52,4196,1697
178 | 1,3,45640,6958,6536,7368,1532,230
179 | 1,3,12759,7330,4533,1752,20,2631
180 | 1,3,11002,7075,4945,1152,120,395
181 | 1,3,3157,4888,2500,4477,273,2165
182 | 1,3,12356,6036,8887,402,1382,2794
183 | 1,3,112151,29627,18148,16745,4948,8550
184 | 1,3,694,8533,10518,443,6907,156
185 | 1,3,36847,43950,20170,36534,239,47943
186 | 1,3,327,918,4710,74,334,11
187 | 1,3,8170,6448,1139,2181,58,247
188 | 1,3,3009,521,854,3470,949,727
189 | 1,3,2438,8002,9819,6269,3459,3
190 | 2,3,8040,7639,11687,2758,6839,404
191 | 2,3,834,11577,11522,275,4027,1856
192 | 1,3,16936,6250,1981,7332,118,64
193 | 1,3,13624,295,1381,890,43,84
194 | 1,3,5509,1461,2251,547,187,409
195 | 2,3,180,3485,20292,959,5618,666
196 | 1,3,7107,1012,2974,806,355,1142
197 | 1,3,17023,5139,5230,7888,330,1755
198 | 1,1,30624,7209,4897,18711,763,2876
199 | 2,1,2427,7097,10391,1127,4314,1468
200 | 1,1,11686,2154,6824,3527,592,697
201 | 1,1,9670,2280,2112,520,402,347
202 | 2,1,3067,13240,23127,3941,9959,731
203 | 2,1,4484,14399,24708,3549,14235,1681
204 | 1,1,25203,11487,9490,5065,284,6854
205 | 1,1,583,685,2216,469,954,18
206 | 1,1,1956,891,5226,1383,5,1328
207 | 2,1,1107,11711,23596,955,9265,710
208 | 1,1,6373,780,950,878,288,285
209 | 2,1,2541,4737,6089,2946,5316,120
210 | 1,1,1537,3748,5838,1859,3381,806
211 | 2,1,5550,12729,16767,864,12420,797
212 | 1,1,18567,1895,1393,1801,244,2100
213 | 2,1,12119,28326,39694,4736,19410,2870
214 | 1,1,7291,1012,2062,1291,240,1775
215 | 1,1,3317,6602,6861,1329,3961,1215
216 | 2,1,2362,6551,11364,913,5957,791
217 | 1,1,2806,10765,15538,1374,5828,2388
218 | 2,1,2532,16599,36486,179,13308,674
219 | 1,1,18044,1475,2046,2532,130,1158
220 | 2,1,18,7504,15205,1285,4797,6372
221 | 1,1,4155,367,1390,2306,86,130
222 | 1,1,14755,899,1382,1765,56,749
223 | 1,1,5396,7503,10646,91,4167,239
224 | 1,1,5041,1115,2856,7496,256,375
225 | 2,1,2790,2527,5265,5612,788,1360
226 | 1,1,7274,659,1499,784,70,659
227 | 1,1,12680,3243,4157,660,761,786
228 | 2,1,20782,5921,9212,1759,2568,1553
229 | 1,1,4042,2204,1563,2286,263,689
230 | 1,1,1869,577,572,950,4762,203
231 | 1,1,8656,2746,2501,6845,694,980
232 | 2,1,11072,5989,5615,8321,955,2137
233 | 1,1,2344,10678,3828,1439,1566,490
234 | 1,1,25962,1780,3838,638,284,834
235 | 1,1,964,4984,3316,937,409,7
236 | 1,1,15603,2703,3833,4260,325,2563
237 | 1,1,1838,6380,2824,1218,1216,295
238 | 1,1,8635,820,3047,2312,415,225
239 | 1,1,18692,3838,593,4634,28,1215
240 | 1,1,7363,475,585,1112,72,216
241 | 1,1,47493,2567,3779,5243,828,2253
242 | 1,1,22096,3575,7041,11422,343,2564
243 | 1,1,24929,1801,2475,2216,412,1047
244 | 1,1,18226,659,2914,3752,586,578
245 | 1,1,11210,3576,5119,561,1682,2398
246 | 1,1,6202,7775,10817,1183,3143,1970
247 | 2,1,3062,6154,13916,230,8933,2784
248 | 1,1,8885,2428,1777,1777,430,610
249 | 1,1,13569,346,489,2077,44,659
250 | 1,1,15671,5279,2406,559,562,572
251 | 1,1,8040,3795,2070,6340,918,291
252 | 1,1,3191,1993,1799,1730,234,710
253 | 2,1,6134,23133,33586,6746,18594,5121
254 | 1,1,6623,1860,4740,7683,205,1693
255 | 1,1,29526,7961,16966,432,363,1391
256 | 1,1,10379,17972,4748,4686,1547,3265
257 | 1,1,31614,489,1495,3242,111,615
258 | 1,1,11092,5008,5249,453,392,373
259 | 1,1,8475,1931,1883,5004,3593,987
260 | 1,1,56083,4563,2124,6422,730,3321
261 | 1,1,53205,4959,7336,3012,967,818
262 | 1,1,9193,4885,2157,327,780,548
263 | 1,1,7858,1110,1094,6818,49,287
264 | 1,1,23257,1372,1677,982,429,655
265 | 1,1,2153,1115,6684,4324,2894,411
266 | 2,1,1073,9679,15445,61,5980,1265
267 | 1,1,5909,23527,13699,10155,830,3636
268 | 2,1,572,9763,22182,2221,4882,2563
269 | 1,1,20893,1222,2576,3975,737,3628
270 | 2,1,11908,8053,19847,1069,6374,698
271 | 1,1,15218,258,1138,2516,333,204
272 | 1,1,4720,1032,975,5500,197,56
273 | 1,1,2083,5007,1563,1120,147,1550
274 | 1,1,514,8323,6869,529,93,1040
275 | 1,3,36817,3045,1493,4802,210,1824
276 | 1,3,894,1703,1841,744,759,1153
277 | 1,3,680,1610,223,862,96,379
278 | 1,3,27901,3749,6964,4479,603,2503
279 | 1,3,9061,829,683,16919,621,139
280 | 1,3,11693,2317,2543,5845,274,1409
281 | 2,3,17360,6200,9694,1293,3620,1721
282 | 1,3,3366,2884,2431,977,167,1104
283 | 2,3,12238,7108,6235,1093,2328,2079
284 | 1,3,49063,3965,4252,5970,1041,1404
285 | 1,3,25767,3613,2013,10303,314,1384
286 | 1,3,68951,4411,12609,8692,751,2406
287 | 1,3,40254,640,3600,1042,436,18
288 | 1,3,7149,2247,1242,1619,1226,128
289 | 1,3,15354,2102,2828,8366,386,1027
290 | 1,3,16260,594,1296,848,445,258
291 | 1,3,42786,286,471,1388,32,22
292 | 1,3,2708,2160,2642,502,965,1522
293 | 1,3,6022,3354,3261,2507,212,686
294 | 1,3,2838,3086,4329,3838,825,1060
295 | 2,2,3996,11103,12469,902,5952,741
296 | 1,2,21273,2013,6550,909,811,1854
297 | 2,2,7588,1897,5234,417,2208,254
298 | 1,2,19087,1304,3643,3045,710,898
299 | 2,2,8090,3199,6986,1455,3712,531
300 | 2,2,6758,4560,9965,934,4538,1037
301 | 1,2,444,879,2060,264,290,259
302 | 2,2,16448,6243,6360,824,2662,2005
303 | 2,2,5283,13316,20399,1809,8752,172
304 | 2,2,2886,5302,9785,364,6236,555
305 | 2,2,2599,3688,13829,492,10069,59
306 | 2,2,161,7460,24773,617,11783,2410
307 | 2,2,243,12939,8852,799,3909,211
308 | 2,2,6468,12867,21570,1840,7558,1543
309 | 1,2,17327,2374,2842,1149,351,925
310 | 1,2,6987,1020,3007,416,257,656
311 | 2,2,918,20655,13567,1465,6846,806
312 | 1,2,7034,1492,2405,12569,299,1117
313 | 1,2,29635,2335,8280,3046,371,117
314 | 2,2,2137,3737,19172,1274,17120,142
315 | 1,2,9784,925,2405,4447,183,297
316 | 1,2,10617,1795,7647,1483,857,1233
317 | 2,2,1479,14982,11924,662,3891,3508
318 | 1,2,7127,1375,2201,2679,83,1059
319 | 1,2,1182,3088,6114,978,821,1637
320 | 1,2,11800,2713,3558,2121,706,51
321 | 2,2,9759,25071,17645,1128,12408,1625
322 | 1,2,1774,3696,2280,514,275,834
323 | 1,2,9155,1897,5167,2714,228,1113
324 | 1,2,15881,713,3315,3703,1470,229
325 | 1,2,13360,944,11593,915,1679,573
326 | 1,2,25977,3587,2464,2369,140,1092
327 | 1,2,32717,16784,13626,60869,1272,5609
328 | 1,2,4414,1610,1431,3498,387,834
329 | 1,2,542,899,1664,414,88,522
330 | 1,2,16933,2209,3389,7849,210,1534
331 | 1,2,5113,1486,4583,5127,492,739
332 | 1,2,9790,1786,5109,3570,182,1043
333 | 2,2,11223,14881,26839,1234,9606,1102
334 | 1,2,22321,3216,1447,2208,178,2602
335 | 2,2,8565,4980,67298,131,38102,1215
336 | 2,2,16823,928,2743,11559,332,3486
337 | 2,2,27082,6817,10790,1365,4111,2139
338 | 1,2,13970,1511,1330,650,146,778
339 | 1,2,9351,1347,2611,8170,442,868
340 | 1,2,3,333,7021,15601,15,550
341 | 1,2,2617,1188,5332,9584,573,1942
342 | 2,3,381,4025,9670,388,7271,1371
343 | 2,3,2320,5763,11238,767,5162,2158
344 | 1,3,255,5758,5923,349,4595,1328
345 | 2,3,1689,6964,26316,1456,15469,37
346 | 1,3,3043,1172,1763,2234,217,379
347 | 1,3,1198,2602,8335,402,3843,303
348 | 2,3,2771,6939,15541,2693,6600,1115
349 | 2,3,27380,7184,12311,2809,4621,1022
350 | 1,3,3428,2380,2028,1341,1184,665
351 | 2,3,5981,14641,20521,2005,12218,445
352 | 1,3,3521,1099,1997,1796,173,995
353 | 2,3,1210,10044,22294,1741,12638,3137
354 | 1,3,608,1106,1533,830,90,195
355 | 2,3,117,6264,21203,228,8682,1111
356 | 1,3,14039,7393,2548,6386,1333,2341
357 | 1,3,190,727,2012,245,184,127
358 | 1,3,22686,134,218,3157,9,548
359 | 2,3,37,1275,22272,137,6747,110
360 | 1,3,759,18664,1660,6114,536,4100
361 | 1,3,796,5878,2109,340,232,776
362 | 1,3,19746,2872,2006,2601,468,503
363 | 1,3,4734,607,864,1206,159,405
364 | 1,3,2121,1601,2453,560,179,712
365 | 1,3,4627,997,4438,191,1335,314
366 | 1,3,2615,873,1524,1103,514,468
367 | 2,3,4692,6128,8025,1619,4515,3105
368 | 1,3,9561,2217,1664,1173,222,447
369 | 1,3,3477,894,534,1457,252,342
370 | 1,3,22335,1196,2406,2046,101,558
371 | 1,3,6211,337,683,1089,41,296
372 | 2,3,39679,3944,4955,1364,523,2235
373 | 1,3,20105,1887,1939,8164,716,790
374 | 1,3,3884,3801,1641,876,397,4829
375 | 2,3,15076,6257,7398,1504,1916,3113
376 | 1,3,6338,2256,1668,1492,311,686
377 | 1,3,5841,1450,1162,597,476,70
378 | 2,3,3136,8630,13586,5641,4666,1426
379 | 1,3,38793,3154,2648,1034,96,1242
380 | 1,3,3225,3294,1902,282,68,1114
381 | 2,3,4048,5164,10391,130,813,179
382 | 1,3,28257,944,2146,3881,600,270
383 | 1,3,17770,4591,1617,9927,246,532
384 | 1,3,34454,7435,8469,2540,1711,2893
385 | 1,3,1821,1364,3450,4006,397,361
386 | 1,3,10683,21858,15400,3635,282,5120
387 | 1,3,11635,922,1614,2583,192,1068
388 | 1,3,1206,3620,2857,1945,353,967
389 | 1,3,20918,1916,1573,1960,231,961
390 | 1,3,9785,848,1172,1677,200,406
391 | 1,3,9385,1530,1422,3019,227,684
392 | 1,3,3352,1181,1328,5502,311,1000
393 | 1,3,2647,2761,2313,907,95,1827
394 | 1,3,518,4180,3600,659,122,654
395 | 1,3,23632,6730,3842,8620,385,819
396 | 1,3,12377,865,3204,1398,149,452
397 | 1,3,9602,1316,1263,2921,841,290
398 | 2,3,4515,11991,9345,2644,3378,2213
399 | 1,3,11535,1666,1428,6838,64,743
400 | 1,3,11442,1032,582,5390,74,247
401 | 1,3,9612,577,935,1601,469,375
402 | 1,3,4446,906,1238,3576,153,1014
403 | 1,3,27167,2801,2128,13223,92,1902
404 | 1,3,26539,4753,5091,220,10,340
405 | 1,3,25606,11006,4604,127,632,288
406 | 1,3,18073,4613,3444,4324,914,715
407 | 1,3,6884,1046,1167,2069,593,378
408 | 1,3,25066,5010,5026,9806,1092,960
409 | 2,3,7362,12844,18683,2854,7883,553
410 | 2,3,8257,3880,6407,1646,2730,344
411 | 1,3,8708,3634,6100,2349,2123,5137
412 | 1,3,6633,2096,4563,1389,1860,1892
413 | 1,3,2126,3289,3281,1535,235,4365
414 | 1,3,97,3605,12400,98,2970,62
415 | 1,3,4983,4859,6633,17866,912,2435
416 | 1,3,5969,1990,3417,5679,1135,290
417 | 2,3,7842,6046,8552,1691,3540,1874
418 | 2,3,4389,10940,10908,848,6728,993
419 | 1,3,5065,5499,11055,364,3485,1063
420 | 2,3,660,8494,18622,133,6740,776
421 | 1,3,8861,3783,2223,633,1580,1521
422 | 1,3,4456,5266,13227,25,6818,1393
423 | 2,3,17063,4847,9053,1031,3415,1784
424 | 1,3,26400,1377,4172,830,948,1218
425 | 2,3,17565,3686,4657,1059,1803,668
426 | 2,3,16980,2884,12232,874,3213,249
427 | 1,3,11243,2408,2593,15348,108,1886
428 | 1,3,13134,9347,14316,3141,5079,1894
429 | 1,3,31012,16687,5429,15082,439,1163
430 | 1,3,3047,5970,4910,2198,850,317
431 | 1,3,8607,1750,3580,47,84,2501
432 | 1,3,3097,4230,16483,575,241,2080
433 | 1,3,8533,5506,5160,13486,1377,1498
434 | 1,3,21117,1162,4754,269,1328,395
435 | 1,3,1982,3218,1493,1541,356,1449
436 | 1,3,16731,3922,7994,688,2371,838
437 | 1,3,29703,12051,16027,13135,182,2204
438 | 1,3,39228,1431,764,4510,93,2346
439 | 2,3,14531,15488,30243,437,14841,1867
440 | 1,3,10290,1981,2232,1038,168,2125
441 | 1,3,2787,1698,2510,65,477,52
442 | 


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/code_in_notes/descriptive_mode.do:
--------------------------------------------------------------------------------
 1 | // descriptive_mode.do
 2 | use datasets/cfps_adult.dta, clear
 3 | drop if qp101<0
 4 | su qp101
 5 | local min_qp101=r(min)
 6 | local max_qp101=r(max)
 7 | local n_group=15
 8 | gen group=floor((qp101-`min_qp101')/(`max_qp101'-`min_qp101'+0.0001)*`n_group')
 9 | tab group
10 | // 样本数最多的组为第9组
11 | di "众数=" `min_qp101'+(9+0.5)/`n_group'*(`max_qp101'-`min_qp101'+0.0001)
12 | 


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/code_in_notes/dgp_mle_censor.ado:
--------------------------------------------------------------------------------
 1 | // dgp_mle_censor.ado 
 2 | // 数据生成过程
 3 | cap program drop dgp_mle_censor
 4 | program dgp_mle_censor
 5 | 	syntax newvarlist(max=1) [, obs(integer 500) mu(real 3.2) sigma2(real 0.5)]
 6 | 	quietly{
 7 | 		clear
 8 | 		set obs `obs'
 9 | 		tempvar xstar x
10 | 		gen `xstar'=sqrt(`sigma2')*rnormal()+`mu'
11 | 		gen `x'= `xstar' if `xstar'<4 & `xstar'>3
12 | 		replace `x'=4 if `xstar'>=4
13 | 		replace `x'=3 if `xstar'<=3
14 | 		gen `varlist'=10^`x'
15 | 	}
16 | end
17 | 


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/code_in_notes/dgp_mle_censor_simulate.do:
--------------------------------------------------------------------------------
 1 | // dgp_mle_censor_simulate.do
 2 | clear
 3 | set seed 8855
 4 | dgp_mle_censor x , obs(500) mu(3.3) sigma2(1)
 5 | hist x
 6 | graph export dgp_mle_censor_hist.pdf, replace
 7 | sort x
 8 | gen p=_n/_N
 9 | line p x, xline(1000 10000, lpattern(dot))
10 | graph export dgp_mle_censor_cdf.pdf, replace
11 | 


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/code_in_notes/empirical_distribution.do:
--------------------------------------------------------------------------------
 1 | // empirical_distribution.do
 2 | clear
 3 | use datasets/cfps_adult.dta
 4 | drop if qp101<0
 5 | // 排序
 6 | sort qp101
 7 | // 生成排序序号
 8 | // 注意qp101中有缺失值，这里不删除缺失值，但是在计算时将其排除
 9 | gen notmissing_qp101=qp101~=.
10 | qui: su notmissing_qp101
11 | gen rank_qp101=_n/r(sum)
12 | // 画图
13 | qui: su qp101, de
14 | local median_qp101=r(p50)
15 | line rank_qp101 qp101, xline(`median_qp101')
16 | graph export empirical_distribution.pdf, replace
17 | 


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/code_in_notes/exponential.do:
--------------------------------------------------------------------------------
1 | // file: exponential.do
2 | set more off
3 | clear
4 | set obs 100
5 | // 产生随机数
6 | gen x=-1*log(runiform())
7 | 


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/code_in_notes/exponential.py:
--------------------------------------------------------------------------------
 1 | #!/usr/bin/python3
 2 | ## file: exponential.py
 3 | 
 4 | # 导入math包，使用math中的log()函数
 5 | import math
 6 | import random as rd
 7 | # 获取5个均匀分布随机数
 8 | x=[-1*math.log(rd.random()) for i in range(5)]
 9 | print(x)
10 | # 导入numpy包，使用其中的log()函数
11 | import numpy as np
12 | import numpy.random as nprd
13 | # 获取5个均匀分布随机数
14 | x=-1*np.log(nprd.random(5))
15 | print(x)
16 | 


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/code_in_notes/gaussian_mixture.do:
--------------------------------------------------------------------------------
 1 | // check_random.do
 2 | set more off
 3 | clear
 4 | set obs 1000
 5 | // generate x1 and x0
 6 | gen x0=rnormal(2.5,sqrt(0.8))
 7 | gen x1=rnormal(-2,1)
 8 | // about 30% patient
 9 | gen d=runiform()<0.7
10 | // generate x
11 | gen x=d*x1+(1-d)*x0
12 | // histogram
13 | hist x
14 | 


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/code_in_notes/gencatutility.ado:
--------------------------------------------------------------------------------
 1 | // gencatutility.ado
 2 | // Chapter 2.6 in Happiness Quantified: a Satisfaction Calculus Approach, van Praag and Ferrer-i-Carbonell
 3 | cap program drop gencatutility
 4 | program define gencatutility
 5 | 	version 16
 6 | 	syntax varname, Gen(name) [Verbose]
 7 | 	tempname level n_levels nl cum cum_nl sum_nl p_nl temp1 temp2 f last_f last_p u uu
 8 | 	local `n_levels' = 0
 9 | 	local `cum'=0
10 | 	local `cum_nl' ""
11 | 	local `sum_nl'=0
12 | 	local `p_nl' ""
13 | 	local `f' ""
14 | 	local `u' ""
15 | 	quietly{
16 | 		levelsof `varlist', local(`level')
17 | 		foreach l of local `level'{
18 | 			sum `varlist' if `varlist' == `l'
19 | 			local `nl' = r(N)
20 | 			local `cum'=``cum''+``nl''
21 | 			local `cum_nl' "``cum_nl'' ``cum''"
22 | 			local `n_levels'=``n_levels''+1
23 | 			local `sum_nl'=``sum_nl''+r(N)
24 | 		}
25 | 		foreach l of local `cum_nl'{
26 | 			local `nl'=`l'/``sum_nl''
27 | 			local `p_nl' "``p_nl'' ``nl''"
28 | 			local `temp1'=invnormal(``nl'')
29 | 			local `temp2'=normalden(``temp1'',0,1)
30 | 			if ``temp1''==.{
31 | 				local `temp2'=0
32 | 			}
33 | 			local `f' "``f'' ``temp2''"
34 | 		}
35 | 		forvalues i=1/``n_levels''{
36 | 			local `temp1': word `i' of ``f''
37 | 			local `temp2': word `i' of ``p_nl''
38 | 			if `i'==1{
39 | 				local `uu'=(0-``temp1'')/(``temp2'')
40 | 				local `u' "``u'' ``uu''"
41 | 				local `last_f'=``temp1''
42 | 				local `last_p'=``temp2''
43 | 			}
44 | 			else{
45 | 				local `uu'=(``last_f''-``temp1'')/(``temp2''-``last_p'')
46 | 				local `u' "``u'' ``uu''"
47 | 				local `last_f'=``temp1''
48 | 				local `last_p'=``temp2''
49 | 			}
50 | 		}
51 | 		gen `gen'=.
52 | 		if "`verbose'" == "verbose"{
53 | 			noisily: di "level --- utility"
54 | 		}
55 | 		forvalues i=1/``n_levels''{
56 | 			local `temp1': word `i' of ``level''
57 | 			local `temp2': word `i' of ``u''
58 | 			replace `gen'=``temp2'' if `varlist'==``temp1''
59 | 			if "`verbose'" == "verbose"{
60 | 				noisily: di "``temp1'' --- ``temp2''"
61 | 			}
62 | 		}
63 | 	}
64 | end
65 | 


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/code_in_notes/geometric_mean.do:
--------------------------------------------------------------------------------
 1 | // geometric_mean.do
 2 | use datasets/hs300index.dta, clear
 3 | // 按照时间排序，用行号作为新的时间
 4 | sort day
 5 | gen t=_n
 6 | tsset t
 7 | // 计算增长率
 8 | gen r=clsindex/L.clsindex
 9 | gen log_r=log(r)
10 | su log_r
11 | local geo_mean=exp(r(mean))
12 | di "几何平均数=`geo_mean'"
13 | di "第一天沪深300指数=" clsindex[1]
14 | di "最后一天沪深300指数=" clsindex[_N]
15 | di "使用几何平均数计算：" clsindex[1]*(`geo_mean'^(_N-1))
16 | 


--------------------------------------------------------------------------------
/code_in_notes/ginindex.do:
--------------------------------------------------------------------------------
 1 | cap program drop ginindex
 2 | program define ginindex, byable(onecall)
 3 |   version 15
 4 |   syntax varlist(max=1), gen(name)
 5 | quietly{
 6 |   if "`_byvars'"==""{
 7 |     tempvar class
 8 |     gen `class'=1
 9 |     local _byvars "`class'"
10 |   }
11 |   // 临时变量
12 |   tempvar rank totalincome cum rat num rect B delta
13 |   // 排序并产生排序变量
14 |   sort `_byvars' `varlist'
15 |   by `_byvars': gen `rank'=_n
16 |   // 产生地区户数、总收入和累积收入及比例
17 |   egen `num'=count(`varlist'), by(`_byvars')
18 |   egen `totalincome'=total(`varlist'), by(`_byvars')
19 |   gen `cum'=`varlist' if `rank'==1
20 |   by `_byvars': replace `cum'=`cum'[_n-1]+`varlist'[_n] if `rank'>1
21 |   gen `rat'=`cum'/`totalincome'
22 |   // 计算每个个体的柱形面积
23 |   by `_byvars': gen `rect'=`rat'/`num'
24 |   // 调整小样本误差，即减去柱子最上面小三角的面积
25 |   gen `delta'=`rat'/2 if `rank'==1
26 |   by `_byvars': replace `delta'=/*
27 |           */  `rat'[_n]-`rat'[_n-1] if `rank'>1
28 |   replace `rect'=`rect'-`delta'/`num'/2
29 |   //最终的指数
30 |   egen `B'=total(`rect'), by(`_byvars')
31 |   gen `gen'=1-2*`B'
32 | }
33 | end
34 | 
35 | use "cfps_family_econ.dta", clear
36 | ginindex fincome1, gen(gini_all)
37 | bysort provcd14: ginindex fincome1, gen(gini)
38 | 


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/code_in_notes/histogram_kdensity.do:
--------------------------------------------------------------------------------
1 | // histogram_kdensity.do
2 | clear
3 | use datasets/cfps_adult.dta
4 | drop if qp101<0
5 | twoway (hist qp101,bin(40) density) (kdensity qp101)
6 | graph export hist_kdens.pdf, replace
7 | 


--------------------------------------------------------------------------------
/code_in_notes/importance_sampling.py:
--------------------------------------------------------------------------------
 1 | ## importance_sampling.py
 2 | import numpy as np
 3 | from numpy import random as nprd
 4 | ##设定参数
 5 | M = 10000
 6 | h1 = lambda x: 0.5 * np.exp(-90 * (x[0] - 0.5)**2 - 45 * (x[1] + 0.1)**2)
 7 | domain = lambda x: (x[0] >= -1) * (x[1] >= -1) * (x[0] <= 1) * (x[1] <= 1)
 8 | pai = lambda x: 1 / 4 * domain(x)
 9 | h1_star = lambda x: 4 * h1(x)
10 | mu1 = 0.5
11 | mu2 = -0.1
12 | sigma1 = np.sqrt(1 / 180)
13 | sigma2 = np.sqrt(1 / 90)
14 | m = lambda x: 1/(2 * np.pi * sigma1 * sigma2) * \
15 |     np.exp(-1 * (x[0]-mu1)**2/(2 * sigma1**2)\
16 |            - (x[1]-mu2)**2 / (2 * sigma2**2))
17 | 
18 | #从m(x)中采样
19 | x = [(nprd.normal(mu1, sigma1), nprd.normal(mu2, sigma2))\
20 |    for i in range(M)]
21 | 
22 | ## 计算积分
23 | H = list(map(lambda x: h1_star(x) * pai(x) / m(x), x))
24 | integral = np.mean(H)
25 | se = np.std(H) / np.sqrt(M)
26 | print("Intgral=", integral)
27 | print("s.e. of Integral=", se)
28 | print("95% C.I.:", integral - 1.96 * se, "~", integral + 1.96 * se)
29 | 
30 | 


--------------------------------------------------------------------------------
/code_in_notes/qqplot_hs300.do:
--------------------------------------------------------------------------------
 1 | // qqplot.do
 2 | clear
 3 | use datasets/hs300index.dta
 4 | // 计算quantile，为了避免出现0和1，减去了0.5
 5 | sort retindex
 6 | gen q=(_n-0.5)/_N
 7 | // 计算均值、标准差
 8 | sum retindex
 9 | local mu=r(mean)
10 | local sd=r(sd)
11 | // 计算正态分布的quantile
12 | gen normal_q = `sd'*invnormal(q)+`mu'
13 | // 画图
14 | twoway (scatter retindex normal_q) /*
15 |     */(line normal_q normal_q), legend(off)
16 | graph export "qqplot_manual_hs300.pdf", replace
17 | // 官方命令
18 | qnorm retindex
19 | graph export "qqplot_hs300.pdf", replace
20 | // 直方图
21 | hist retindex, norm
22 | graph export "hist_hs300.pdf", replace
23 | 


--------------------------------------------------------------------------------
/code_in_notes/rejection.py:
--------------------------------------------------------------------------------
 1 | #!/usr/bin/python3
 2 | ## file: rejection.py
 3 | import numpy as np
 4 | import numpy.random as nprd
 5 | import scipy.special as scisp
 6 | ## 设定参数
 7 | c=3 #抽取大于5的正态分布样本
 8 | N=1000 #抽取200个
 9 | ## 直接使用正态分布进行拒绝抽样
10 | times=0 #产生了多少次正态分布
11 | accept=0 #接受了多少个
12 | sample1=[] #结果
13 | while accept<N:
14 |     x=nprd.normal()
15 |     if x>=c:
16 |         sample1.append(x)
17 |         accept=accept+1
18 |     times=times+1
19 | print("接受率=",N/times)
20 | 
21 | ## 使用指数分布进行拒绝抽样
22 | times=0 #产生了多少次指数分布
23 | accept=0 #接受了多少个
24 | sample2=[] #结果
25 | # 计算参数
26 | lam=(c+np.sqrt(c**2+4))/2
27 | M=np.exp((lam**2-2*lam*c)/2)/(np.sqrt(2*np.pi)* \
28 |     lam*(1-scisp.ndtr(c)))
29 | normal_m=1/np.sqrt(2*np.pi) #正态分布密度函数前面的常数
30 | # 截断正态分布密度函数
31 | f_trunc_normal = lambda x: \
32 |     normal_m*np.exp(-0.5*x**2)/(1-scisp.ndtr(c))
33 | # 指数分布密度函数
34 | f_exponential = lambda x: lam*np.exp(-1*lam*(x-c))
35 | while accept<N:
36 |     ## 产生指数分布
37 |     x=c-np.log(nprd.uniform())/lam
38 |     ## 接受概率
39 |     r=f_trunc_normal(x)/(M*f_exponential(x))
40 |     if nprd.uniform()<=r:
41 |         sample2.append(x)
42 |         accept=accept+1
43 |     times=times+1
44 | print("接受率=",N/times)
45 | 


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/code_in_notes/rejection_beta.do:
--------------------------------------------------------------------------------
 1 | // rejection_beta.do
 2 | clear
 3 | set obs 10000
 4 | set seed 505
 5 | local alpha=4
 6 | local beta=2
 7 | // 求密度函数极值
 8 | local M=betaden(`alpha',`beta',(`alpha'-1)/(`alpha'+`beta'-2))
 9 | gen u=runiform()*`M'
10 | gen x=runiform()
11 | // 计算密度函数
12 | gen density=betaden(`alpha',`beta',x)
13 | // 抽样
14 | keep if u<density
15 | // 查看抽样的描述性统计
16 | su x


--------------------------------------------------------------------------------
/code_in_notes/rejection_beta.py:
--------------------------------------------------------------------------------
 1 | #!/usr/bin/python3
 2 | ## file: rejection_beta.py
 3 | import numpy as np
 4 | import numpy.random as nprd
 5 | import scipy.special as scisp
 6 | # 设定参数
 7 | alpha = 4
 8 | beta = 2
 9 | # beta分布密度函数
10 | f=lambda x: 1/scisp.beta(alpha,beta)* \
11 |     x**(alpha-1) * (1-x)**(beta-1)
12 | # 计算密度函数最大值
13 | M = f((1 - alpha) / (2 - alpha - beta))
14 | print(M)
15 | # 随机抽两个均匀分布，一个为(0,1)，一个为(0,M)，抽500个
16 | N = 500
17 | x = nprd.random(N)
18 | u = nprd.random(N) * M
19 | # 挑出使得u<beta密度函数的x
20 | accepted = [i for i in range(N) if u[i] <= f(x[i])]
21 | rand_beta = x[accepted]  #生成的Beta分布随机数
22 | rand_U_selected = u[accepted]
23 | # 画图
24 | import matplotlib.pyplot as plt
25 | # 设定图像大小和坐标范围
26 | plt.rcParams['figure.figsize'] = (8.0, 5.0)
27 | plt.xlim(0, 1)
28 | plt.ylim(0, M + 0.1)
29 | # 横线和竖线
30 | x_grid = np.linspace(0, 1, 100)  #(0,1)均匀的100个点
31 | y_M = np.ones(100) * M
32 | beta_dens = f(x_grid)
33 | y1 = np.linspace(0, f(0.4), 20)
34 | y2 = np.linspace(f(0.4), M, 20)
35 | x_hline = np.ones(20) * 0.4
36 | plt.xlabel(r'$X$')
37 | plt.ylabel(r'$U$')
38 | plt.title('Sampling from Beta dist.')  # 标题
39 | ## 画出散点图
40 | plt.scatter(x, u, color='blue', s=0.8)
41 | plt.scatter(rand_beta, rand_U_selected, color='black', s=0.8)
42 | plt.plot(x_grid, y_M, color='red')  ## 最大值
43 | plt.plot(x_grid, beta_dens, color='orange')  ## 密度函数
44 | plt.plot(x_hline, y1, color='grey')  ## 接受区域
45 | plt.text(0.42, 0.3, "Acceptance", fontsize=15, horizontalalignment="left")
46 | plt.plot(x_hline, y2, color='pink')  ## 拒绝区域
47 | plt.text(0.38, 1.5, "Rejection", fontsize=15, horizontalalignment="right")
48 | plt.savefig("rejection_beta.pdf")


--------------------------------------------------------------------------------
/code_in_notes/rejection_trunc.do:
--------------------------------------------------------------------------------
 1 | // rejection_trunc.do
 2 | clear
 3 | set more off
 4 | set seed 505
 5 | set obs 1000
 6 | // 参数
 7 | scalar c=3
 8 | // 计算lambda和M
 9 | scalar pi=3.1415926
10 | scalar temp_cons=sqrt(2*pi)*(1-normal(c))
11 | scalar lam=2.5 // scalar lam=(c+sqrt(c^2+4))/2
12 | scalar M=(exp(lam^2/2-lam*c-log(lam)))/temp_cons
13 | // 产生均匀分布和指数分布
14 | gen x=c-log(runiform())/lam
15 | gen u=runiform()
16 | // 截断正态分布密度函数
17 | gen density=normalden(x)/(1-normal(c))
18 | label variable density "f(x)"
19 | // 指数分布密度函数（用M标准化，即 M*g(x)）
20 | gen density_exp=M*lam*exp(-1*lam*(x-c))
21 | label variable density_exp "M*g(x)"
22 | // 挑出使得u<l/(M*g)的x，
23 | gen selected=u<=(density/density_exp)
24 | // 画图
25 | sort x
26 | // 显示方便，散点图y轴用标准化的密度函数值乘以u
27 | gen u_y=u*density_exp
28 | twoway (line density_exp x, lpattern(dash)) ///
29 |      (line density x, lc(black)) ///
30 |      (scatter u_y x if selected==0, msize(small) msymbol(x) mc(gs8)) ///
31 |      (scatter u_y x if selected==1, msize(small) msymbol(v) mc(gs10)) ///
32 |      , legend(on ring(0) pos(1)  ///
33 |      label(3 "Rejected") label(4 "Accepted") ///
34 |      label(2 "Density of Accepted")) ///
35 |      graphr(fcolor(white) color(white))
36 | graph export rejection_trunc.pdf, replace
37 | 


--------------------------------------------------------------------------------
/code_in_notes/rejection_trunc_optimal.do:
--------------------------------------------------------------------------------
 1 | // rejection_trunc_optimal.do
 2 | clear
 3 | set more off
 4 | set seed 505
 5 | set obs 1000
 6 | // 参数
 7 | scalar c=3
 8 | // 计算lambda和M
 9 | scalar pi=3.1415926
10 | scalar temp_cons=sqrt(2*pi)*(1-normal(c))
11 | // 最优lambda
12 | scalar lam=(c+sqrt(c^2+4))/2
13 | scalar M=(exp(lam^2/2-lam*c-log(lam)))/temp_cons
14 | // 产生均匀分布和指数分布
15 | gen x=c-log(runiform())/lam
16 | gen u=runiform()
17 | // 截断正态分布密度函数
18 | gen density=normalden(x)/(1-normal(c))
19 | label variable density "f(x)"
20 | // 指数分布密度函数（用M标准化，即 M*g(x)）
21 | gen density_exp=M*lam*exp(-1*lam*(x-c))
22 | label variable density_exp "M*g(x)"
23 | // 挑出使得u<l/(M*g)的x，
24 | gen selected=u<=(density/density_exp)
25 | // 画图
26 | sort x
27 | // 显示方便，散点图y轴用标准化的密度函数值乘以u
28 | gen u_y=u*density_exp
29 | twoway (line density_exp x, lpattern(dash)) ///
30 |      (line density x, lc(black)) ///
31 |      (scatter u_y x if selected==0, msize(small) msymbol(x) mc(gs8)) ///
32 |      (scatter u_y x if selected==1, msize(small) msymbol(v) mc(gs10)) ///
33 |      , legend(on ring(0) pos(1)  ///
34 |      label(3 "Rejected") label(4 "Accepted") ///
35 |      label(2 "Density of Accepted")) ///
36 |      graphr(fcolor(white) color(white))
37 | graph export rejection_trunc_optimal.pdf, replace
38 | 


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/code_in_notes/scatter_weight_height.do:
--------------------------------------------------------------------------------
1 | // scatter_weight_height.do
2 | clear
3 | use datasets/cfps_adult.dta
4 | drop if qp101<0
5 | drop if qp102<0
6 | twoway (scatter qp102 qp101 if mod(_n,10)==0) (lfit qp102 qp101), legend(pos(11) ring(0) label(1 "体重") label(2 "拟合"))
7 | graph export scatter_weight_height.pdf, replace
8 | 


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/code_in_notes/simulate_CLT.do:
--------------------------------------------------------------------------------
 1 | // simulate_CLT.do
 2 | clear all
 3 | set more off
 4 | set seed 8855
 5 | // 混合正态分布
 6 | set obs 1000
 7 | gen d=runiform()>=0.5
 8 | gen x=d*rnormal(3,1)+(1-d)*rnormal(-3,1)
 9 | hist x
10 | graph export simulate_CLT_mix.pdf, replace
11 | // 模拟
12 | local graphs ""
13 | foreach N in 2 3 4 10 100 1000{
14 | 	frame create mean`N' m
15 | 	frame mean`N': label variable m "样本均值"
16 | 	forvalues j=1/2000{
17 | 		clear
18 | 		set obs `N'
19 | 		gen d=runiform()>=0.5
20 | 		gen x=d*rnormal(3,1)+(1-d)*rnormal(-3,1)
21 | 		su x
22 | 		frame post mean`N' (r(mean))
23 | 	}
24 | 	frame mean`N': hist m, normal saving(simulate_CLT`N', replace) title("N=`N'")
25 | 	local graphs "`graphs' simulate_CLT`N'.gph"
26 | }
27 | graph combine `graphs', col(3)
28 | graph export simulate_CLT.pdf, replace
29 | 


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/code_in_notes/simulate_CLT.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | from numpy import random as nprd
 3 | 
 4 | 
 5 | def sampling(N):
 6 |     ## 产生一组样本，以0.5的概率为z+3，0.5的概率为z-3，其中z~N(0,1)
 7 |     d = nprd.rand(N) < 0.5
 8 |     z = nprd.randn(N)
 9 |     x = np.array([z[i] + 3 if d[i] else z[i] - 3 for i in range(N)])
10 |     return x
11 | 
12 | 
13 | N = [2, 3, 4, 10, 100, 1000]  # sample size
14 | M = 2000
15 | MEANS = []
16 | for n in N:
17 |     mean_x = np.zeros(M)
18 |     for i in range(M):
19 |         x = sampling(n)
20 |         mean_x[i] = np.mean(x) / np.sqrt(10 / n)  ## 标准化，因为var(x)=10
21 |     MEANS.append(mean_x)
22 | 
23 | ## 导入matplotlib
24 | import matplotlib.pyplot as plt
25 | 
26 | # 设定图像大小
27 | plt.rcParams['figure.figsize'] = (10.0, 8.0)
28 | 
29 | x = sampling(1000)
30 | plt.xlabel('x')
31 | plt.ylabel('Density')
32 | plt.title('Histogram of Mixed Normal')
33 | plt.hist(x, bins=30, density=True)  ## histgram
34 | plt.savefig("simulate_CLT_mix.pdf")
35 | plt.show() 
36 | 
37 | ## 均值
38 | ax1 = plt.subplot(2, 3, 1)
39 | ax2 = plt.subplot(2, 3, 2)
40 | ax3 = plt.subplot(2, 3, 3)
41 | ax4 = plt.subplot(2, 3, 4)
42 | ax5 = plt.subplot(2, 3, 5)
43 | ax6 = plt.subplot(2, 3, 6)
44 | 
45 | ## normal density
46 | x = np.linspace(-3, 3, 100)
47 | d = [1.0 / np.sqrt(2 * np.pi) * np.exp(-i**2 / 2) for i in x]
48 | 
49 | 
50 | def plot_density(ax, data, N):
51 |     ax.hist(data, bins=30, density=True)  ## histgram
52 |     ax.plot(x, d)
53 |     ax.set_title(r'Histogram of $\bar{x}$:N=%d' % N)
54 | 
55 | 
56 | plot_density(ax1, MEANS[0], N[0])
57 | plot_density(ax2, MEANS[1], N[1])
58 | plot_density(ax3, MEANS[2], N[2])
59 | plot_density(ax4, MEANS[3], N[3])
60 | plot_density(ax5, MEANS[4], N[4])
61 | plot_density(ax6, MEANS[5], N[5])
62 | plt.savefig("simulate_CLT.pdf")
63 | plt.show() 


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/code_in_notes/simulate_LLN.do:
--------------------------------------------------------------------------------
 1 | // simulate_LLN.do
 2 | clear
 3 | set more off
 4 | set seed 8855
 5 | local M=5000
 6 | set obs `M'
 7 | gen u=runiform()
 8 | gen x=u>=0.5
 9 | gen x_bar=.
10 | forvalues i=1/`M'{
11 | 	qui{
12 | 		su x if _n<=`i'
13 | 		replace x_bar = r(mean) if _n==`i'
14 | 	}
15 | }
16 | gen n=_n
17 | line x_bar n, yline(0.5)
18 | graph export simulate_LLN.pdf, replace
19 | 


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/code_in_notes/simulate_LLN.py:
--------------------------------------------------------------------------------
 1 | import numpy as np
 2 | from numpy import random as nprd
 3 | 
 4 | True_P = 0.5
 5 | 
 6 | 
 7 | def sampling(N):
 8 |     ## 产生Bernouli样本
 9 |     x = nprd.rand(N) < True_P
10 |     return x
11 | 
12 | 
13 | M = 10000  #模拟次数
14 | xbar = np.zeros(M)
15 | N = np.array([i + 1 for i in range(M)])
16 | x = sampling(M)
17 | for i in range(M):
18 |     if i == 0:
19 |         xbar[i] = x[i]
20 |     else:
21 |         xbar[i] = (x[i] + xbar[i - 1] * i) / (i + 1)
22 | 
23 | ## 导入matplotlib
24 | import matplotlib.pyplot as plt
25 | # 设定图像大小
26 | plt.rcParams['figure.figsize'] = (10.0, 8.0)
27 | 
28 | plt.plot(N, xbar, label=r'$\bar{x}$', color='pink')  ## xbar
29 | xtrue = np.ones(M) * True_P
30 | plt.plot(N, xtrue, label=r'$0.5$', color='black')  ## true xbar
31 | plt.xlabel('N')
32 | plt.ylabel(r'$\bar{x}$')
33 | plt.legend(loc='upper right', frameon=True)
34 | plt.savefig("simulate_LLN.pdf")
35 | plt.show() 


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/code_in_notes/simulation_lm_ols_test.do:
--------------------------------------------------------------------------------
 1 | // simulation_lm_ols_test.do
 2 | clear
 3 | set more off
 4 | set seed 42
 5 | // test statistic
 6 | cap program drop ols_lm_test_stat
 7 | program define ols_lm_test_stat, rclass
 8 | 	syntax [,obs(integer 100) beta(real 0) alpha(real 1) sigma(real 1)]
 9 | 	clear
10 | 	tempvar x y e xe
11 | 	quietly{
12 | 		set obs `obs'
13 | 		gen `x'=rnormal(0,2)
14 | 		gen `y'=`x'*`beta'+`alpha'+rnormal(0,`sigma')
15 | 		su `y'
16 | 		gen `e'=`y'-r(mean)
17 | 		gen `xe'=`x'*`e'
18 | 		sum `xe'
19 | 		return scalar chi2_stat=(r(sum)^2)/(`obs'*r(Var))
20 | 	}
21 | end
22 | // upper tail of chi2(1)
23 | local cv=invchi2tail(1,0.05)
24 | // simulation under H0
25 | simulate chi2=r(chi2_stat),reps(5000): ols_lm_test_stat
26 | gen density=chi2den(1,chi2) if chi2>0.1
27 | sort chi2
28 | twoway (hist chi2, density) (line density chi2), xline(`cv')
29 | graph export simulation_lm_ols_test0.pdf, replace
30 | gen p_005=chi2>=`cv'
31 | su p_005
32 | // simulation under H1
33 | clear
34 | simulate chi2=r(chi2_stat),reps(5000): ols_lm_test_stat, beta(0.2)
35 | gen density=chi2den(1,chi2) if chi2>0.1
36 | sort chi2
37 | twoway (hist chi2, density) (line density chi2), xline(`cv')
38 | graph export simulation_lm_ols_test1.pdf, replace
39 | gen p_005=chi2>=`cv'
40 | su p_005
41 | 


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/code_in_notes/simulation_lm_test.do:
--------------------------------------------------------------------------------
 1 | // simulation_lm_test.do
 2 | clear
 3 | set more off
 4 | set seed 42
 5 | // test statistic
 6 | cap program drop lm_test_stat
 7 | program define lm_test_stat, rclass
 8 | 	syntax [,obs(integer 100) lambda(real 10)]
 9 | 	clear
10 | 	tempvar x x_10
11 | 	quietly{
12 | 		set obs `obs'
13 | 		gen `x'=rpoisson(`lambda')
14 | 		gen `x_10'=`x'-10
15 | 		su `x_10'
16 | 		return scalar chi2_stat=(r(sum))^2/(`obs'*10)
17 | 	}
18 | end
19 | // upper tail of chi2(1)
20 | local cv=invchi2tail(1,0.05)
21 | // simulation under H0
22 | simulate chi2=r(chi2_stat),reps(5000): lm_test_stat
23 | gen density=chi2den(1,chi2) if chi2>0.1
24 | sort chi2
25 | twoway (hist chi2, density) (line density chi2), xline(`cv')
26 | graph export simulation_lm_test0.pdf, replace
27 | gen p_005=chi2>=`cv'
28 | su p_005
29 | // simulation under H1
30 | clear
31 | simulate chi2=r(chi2_stat),reps(5000): lm_test_stat, lambda(11.5)
32 | gen density=chi2den(1,chi2) if chi2>0.1
33 | sort chi2
34 | twoway (hist chi2, density) (line density chi2), xline(`cv')
35 | graph export simulation_lm_test1.pdf, replace
36 | gen p_005=chi2>=`cv'
37 | su p_005
38 | 


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/code_in_notes/simulation_lr_test.do:
--------------------------------------------------------------------------------
 1 | // simulation_lr_test.do
 2 | clear
 3 | set more off
 4 | set seed 42
 5 | // test statistic
 6 | cap program drop lr_test_stat
 7 | program define lr_test_stat, rclass
 8 | 	syntax [,obs(integer 100) lambda(real 1)]
 9 | 	clear
10 | 	tempvar x
11 | 	quietly{
12 | 		set obs `obs'
13 | 		gen `x'=rpoisson(`lambda')
14 | 		su `x'
15 | 		return scalar chi2_stat=2*`obs'*(log(r(mean))*r(mean)-r(mean)+1)
16 | 	}
17 | end
18 | // upper tail of chi2(1)
19 | local cv=invchi2tail(1,0.05)
20 | // simulation under H0
21 | simulate chi2=r(chi2_stat),reps(5000): lr_test_stat
22 | gen density=chi2den(1,chi2) if chi2>0.1
23 | sort chi2
24 | twoway (hist chi2, density) (line density chi2), xline(`cv')
25 | graph export simulation_lr_test0.pdf, replace
26 | gen p_005=chi2>=`cv'
27 | su p_005
28 | // simulation under H1
29 | clear
30 | simulate chi2=r(chi2_stat),reps(5000): lr_test_stat, lambda(1.5)
31 | gen density=chi2den(1,chi2) if chi2>0.1
32 | sort chi2
33 | twoway (hist chi2, density) (line density chi2), xline(`cv')
34 | graph export simulation_lr_test1.pdf, replace
35 | gen p_005=chi2>=`cv'
36 | su p_005
37 | 


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/code_in_notes/simulation_wald_test.do:
--------------------------------------------------------------------------------
 1 | // simulation_wald_test.do
 2 | clear
 3 | set more off
 4 | set seed 42
 5 | // test statistic
 6 | cap program drop wald_test_stat
 7 | program define wald_test_stat, rclass
 8 | 	syntax [,obs(integer 100) mu(real -1) sigma2(real 1)]
 9 | 	clear
10 | 	tempvar x
11 | 	quietly{
12 | 		set obs `obs'
13 | 		gen `x'=rnormal(`mu',sqrt(`sigma2'))
14 | 		su `x'
15 | 		return scalar chi2_stat=`obs'*(r(mean)^2-1)^2/(4*r(mean)^2*r(Var))
16 | 	}
17 | end
18 | // upper tail of chi2(1)
19 | local cv=invchi2tail(1,0.05)
20 | // simulation under H0
21 | simulate chi2=r(chi2_stat),reps(5000): wald_test_stat
22 | gen density=chi2den(1,chi2) if chi2>0.1
23 | sort chi2
24 | twoway (hist chi2, density) (line density chi2), xline(`cv')
25 | graph export simulation_wald_test0.pdf, replace
26 | gen p_005=chi2>=`cv'
27 | su p_005
28 | // simulation under H1
29 | clear
30 | simulate chi2=r(chi2_stat),reps(5000): wald_test_stat, mu(1.5)
31 | gen density=chi2den(1,chi2) if chi2>0.1
32 | sort chi2
33 | twoway (hist chi2, density) (line density chi2), xline(`cv')
34 | graph export simulation_wald_test1.pdf, replace
35 | gen p_005=chi2>=`cv'
36 | su p_005
37 | 


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/code_in_notes/st_call_py_tree.do:
--------------------------------------------------------------------------------
 1 | clear
 2 | set more off
 3 | use datasets/soep_female_labor.dta
 4 | 
 5 | // 定义变量
 6 | local y "employment"
 7 | local controls "chld6 chld16 age income husworkhour husemployment region edu husedu"
 8 | 
 9 | // 首先做logit回归做初步探索
10 | logit `y' `controls'
11 | predict ps_employment_logit
12 | gen predict_employment_logit = ps_employment_logit>=0.5
13 | gen accuracy_logit = employment == predict_employment_logit
14 | 
15 | //放到Python中去做回归树
16 | python
17 | import numpy as np
18 | import pandas as pd
19 | from sfi import Data, Macro, Missing
20 | def stata2numpy(varname):
21 |     data=Data.get(varname)
22 |     x=[d if not Missing.isMissing(d) else np.nan for d in data]
23 |     return np.array(x)
24 | 
25 | y_var_name = Macro.getLocal("y")
26 | x_var_name = Macro.getLocal("controls").split(" ")
27 | y=stata2numpy(y_var_name)
28 | X=pd.DataFrame()
29 | for x in x_var_name:
30 |     X[x]=stata2numpy(x)
31 | print(X)
32 | from sklearn import tree
33 | dtree=tree.DecisionTreeClassifier(max_depth=10) ##设定最大深度
34 | dtree.fit(X,y) ##训练
35 | prob_df=dtree.predict_proba(X)[:,1]
36 | pred_df=dtree.predict(X)
37 | 
38 | def array2stata(npname):
39 |     return [n if np.isfinite(n) else Missing.getValue() for n in npname]
40 | 
41 | prob=array2stata(prob_df)
42 | pred=array2stata(pred_df)
43 | Data.addVarDouble("predict_employment_tree")
44 | Data.addVarDouble("ps_employment_tree")
45 | Data.store("predict_employment_tree",None,pred)
46 | Data.store("ps_employment_tree",None,prob)
47 | end
48 | 
49 | gen accuracy_tree = employment == predict_employment_tree
50 | su accuracy_logit accuracy_tree


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/code_in_notes/standard_normal_mean.do:
--------------------------------------------------------------------------------
 1 | // standard_normal_mean.do
 2 | clear
 3 | set more off
 4 | cap program drop std_normal_mean
 5 | program define std_normal_mean, rclass
 6 | 	version 12
 7 | 	syntax [,obs(integer 10) mu(real 0) sigma(real 1)]
 8 | 	drop _all
 9 | 	set obs `obs'
10 | 	tempvar x
11 | 	gen `x'=`sigma'*rnormal()+`mu'
12 | 	su `x'
13 | 	return scalar mean1=sqrt(`obs')*(r(mean)-`mu')/`sigma'
14 | 	return scalar mean2=sqrt(`obs')*(r(mean)-`mu')/r(sd)
15 | end
16 | local N=8
17 | local df=`N'-1
18 | simulate std_mean=r(mean1) sample_mean=r(mean2), reps(20000): std_normal_mean, obs(`N')
19 | 
20 | // standardised with sigma
21 | sort std_mean
22 | gen normal_den_std_mean=normalden(std_mean)
23 | label variable normal_den_std_mean "Std Normal Density"
24 | gen student_den_std_mean=tden(`df',std_mean)
25 | label variable student_den_std_mean "t(`df') Density"
26 | twoway (hist std_mean, density) (line normal_den_std_mean std_mean) (line student_den_std_mean std_mean) , graphr(fcolor(white) color(white))  xtitle("") saving(standard_normal_mean_1, replace)
27 | 
28 | // standardised with std deviation
29 | sort sample_mean
30 | gen normal_den_std_mean2=normalden(sample_mean)
31 | label variable normal_den_std_mean2 "Std Normal Density"
32 | gen t_den_std_sample_mean=tden(`df',sample_mean)
33 | label variable t_den_std_sample_mean "t(`df') Density"
34 | twoway (hist sample_mean, density) (line normal_den_std_mean2 sample_mean) (line t_den_std_sample_mean sample_mean), graphr(fcolor(white) color(white)) xtitle("") saving(standard_normal_mean_2, replace)
35 | 
36 | graph combine standard_normal_mean_1.gph standard_normal_mean_2.gph, graphr(fcolor(white) color(white)) col(2)
37 | graph export standard_normal_mean.pdf, replace
38 | 


--------------------------------------------------------------------------------
/code_in_notes/standard_normal_var.do:
--------------------------------------------------------------------------------
 1 | // standard_normal_var.do
 2 | cap program drop std_normal_var
 3 | program define std_normal_var, rclass
 4 | 	version 12
 5 | 	syntax [,obs(integer 10) mu(real 0) sigma(real 1)]
 6 | 	drop _all
 7 | 	set obs `obs'
 8 | 	tempvar x
 9 | 	gen `x'=`sigma'*rnormal()+`mu'
10 | 	su `x'
11 | 	return scalar std_var=(`obs'-1)*r(Var)/(`sigma'^2)
12 | end
13 | 
14 | simulate std_var=r(std_var), reps(20000): std_normal_var
15 | 
16 | 
17 | sort std_var
18 | gen chi2_den=chi2den(9,std_var)
19 | label variable chi2_den "Chi2 Density"
20 | twoway (hist std_var, density) (line chi2_den std_var), graphr(fcolor(white) color(white)) xtitle("")
21 | graph export standard_normal_var.pdf, replace
22 | 


--------------------------------------------------------------------------------
/code_in_notes/statistic_mean.do:
--------------------------------------------------------------------------------
 1 | // statistic_mean.do
 2 | clear all
 3 | set seed 19880505
 4 | frame create means m
 5 | forvalues i=1/10000{
 6 |     clear
 7 |     set obs 100
 8 |     gen x=rnormal(1,2)
 9 |     qui: su x
10 |     frame post means (r(mean))
11 | }
12 | frame change means
13 | su m
14 | hist m
15 | graph export statistc_mean.pdf, replace
16 | 


--------------------------------------------------------------------------------
/code_in_notes/test_power_function.do:
--------------------------------------------------------------------------------
 1 | // test_power_function.do
 2 | clear
 3 | set more off
 4 | 
 5 | ** test under H0: mu=mu0 at 5% significant level
 6 | cap program drop test_normal_mean
 7 | program define test_normal_mean, rclass
 8 | 	version 12
 9 | 	syntax [,obs(integer 10) mu(real 0) mu0(real 0) sigma(real 1)]
10 | 	drop _all
11 | 	set obs `obs'
12 | 	tempvar x
13 | 	gen `x'=`sigma'*rnormal()+`mu'
14 | 	quietly: su `x'
15 | 	tempname std_mean rejected
16 | 	scalar `std_mean'=sqrt(`obs')*(r(mean)-`mu0')/r(sd)
17 | 	di `std_mean'
18 | 	if abs(`std_mean')>invt(`obs'-1,1-0.05/2){
19 | 		scalar `rejected'=1
20 | 	}
21 | 	else{
22 | 		scalar `rejected'=0
23 | 	}
24 | 	return scalar rejected=`rejected'
25 | end
26 | 
27 | ** replicate test for 1000 times by default
28 | cap program drop compute_power
29 | program define compute_power, rclass
30 | 	version 12
31 | 	syntax [,obs(integer 10) mu(real 0) mu0(real 0)/*
32 | 		*/ sigma(real 1) reps(integer 1000)]
33 | 	quietly{
34 | 	preserve // 缓存内存中现有的变量
35 | 	drop _all
36 | 	simulate rejected=r(rejected),reps(`reps'):/*
37 | 		*/ test_normal_mean, obs(`obs') mu(`mu')/*
38 | 		*/ mu0(`mu0') sigma(`sigma')
39 | 	quietly: su rejected
40 | 	return scalar power=r(mean)
41 | 	restore // 恢复preserve之前内存变量
42 | 	}
43 | end
44 | 
45 | ** draw power function for sample size=[5 30 100]
46 | set obs 100
47 | gen mu=-3+(_n-1)*6/99
48 | tempname mu
49 | gen power5=.
50 | gen power30=.
51 | gen power100=.
52 | foreach ss in 5 30 100{
53 |     forvalues i= 1/100{
54 |         ** mu in [-3,3]
55 |         local `mu'=-3+(`i'-1)*6/99
56 | 	compute_power, mu(``mu'') obs(`ss')
57 | 	replace power`ss'=r(power) in `i'
58 |     }
59 | }
60 | label variable mu "Ture value of mu"
61 | label variable  power5 "Power 5 Samples"
62 | label variable  power30 "Power 30 Samples"
63 | label variable  power100 "Power 100 Samples"
64 | twoway (line power5 mu, lpattern(solid))/*
65 | 	*/ (line power30 mu, lpattern(dash))/*
66 | 	*/ (line power100 mu, lpattern(dot))
67 | graph export power_function.pdf, replace
68 | 


--------------------------------------------------------------------------------
/code_in_notes/test_under_null.do:
--------------------------------------------------------------------------------
 1 | // test_under_null.do
 2 | clear
 3 | set more off
 4 | set seed 880505
 5 | // test under H0: mu=mu0 at 5% significant level
 6 | cap program drop test_normal_mean
 7 | program define test_normal_mean, rclass
 8 | 	version 12
 9 | 	syntax [,obs(integer 10) mu(real 0) mu0(real 0) sigma(real 1)]
10 | 	drop _all
11 | 	set obs `obs'
12 | 	tempvar x
13 | 	gen `x'=`sigma'*rnormal()+`mu'
14 | 	quietly: su `x'
15 | 	tempname std_mean rejected
16 | 	scalar `std_mean'=sqrt(`obs')*(r(mean)-`mu0')/r(sd)
17 | 	di `std_mean'
18 | 	if abs(`std_mean')>invt(`obs'-1,1-0.05/2){
19 | 		scalar `rejected'=1
20 | 	}
21 | 	else{
22 | 		scalar `rejected'=0
23 | 	}
24 | 	return scalar rejected=`rejected'
25 | end
26 | 
27 | simulate rejected=r(rejected),reps(10000): test_normal_mean
28 | su rejected
29 | 


--------------------------------------------------------------------------------
/code_in_notes/ttest_mean_comparison.do:
--------------------------------------------------------------------------------
1 | // t-test of two means comparison
2 | use datasets/cfps_adult.dta, clear
3 | gen log_income=log(1+p_income)
4 | // 方差相同假设下的检验
5 | ttest log_income, by(cfps_gender)
6 | // 方差不相同假设下的检验
7 | ttest log_income, by(cfps_gender) unequal
8 | // 方差不相同的假设下比较
9 | 


--------------------------------------------------------------------------------
/code_in_notes/twosls_by_hand.do:
--------------------------------------------------------------------------------
 1 | // 2SLS by hand
 2 | cap program drop twosls
 3 | program twosls, eclass
 4 | 	version 15.0
 5 | 	syntax varlist(max=1), endo(varlist) instru(varlist) /*
 6 | 		*/control(varlist)
 7 | 	tempname dep Xhat XhhX pred_endo pred_var b sigma2 V
 8 | 	tempvar resid
 9 | 	local `dep' "`varlist'"
10 | 	quietly{
11 | 		// get the predicted value of endo x
12 | 		local `pred_var' ""
13 | 		foreach x of varlist `endo'{
14 | 			reg `x' `instru' `control'
15 | 			predict `pred_endo'_`x'
16 | 			local `pred_var' "``pred_var'' `pred_endo'_`x'"
17 | 		}
18 | 		local `Xhat' "``pred_var'' `control'"
19 | 		// ols of y on Xhat, get b
20 | 		reg ``dep'' ``Xhat''
21 | 		matrix `b'=e(b)
22 | 		mat colnames `b'= `endo' `control' _cons
23 | 		///// compute variance under homoskedasticity
24 | 		// first compute residuals
25 | 		gen `resid'=``dep''
26 | 		foreach x of varlist `endo' `control'{
27 | 			replace `resid'=`resid'-`b'[1,colnumb(`b',"`x'")]*`x'
28 | 		}
29 | 		replace `resid'=`resid'-`b'[1,colnumb(`b',"_cons")]
30 | 		su `resid'
31 | 		scalar `sigma2'=r(Var)
32 | 		// then compute XhhX
33 | 		matrix accum `XhhX'=``Xhat''
34 | 		matrix `V'=`sigma2'*invsym(`XhhX')
35 | 		mat colnames `V'= `endo' `control' _cons
36 | 		mat rownames `V'= `endo' `control' _cons
37 | 		drop ``pred_var''
38 | 	}
39 | 	ereturn clear
40 | 	ereturn post `b' `V'
41 | 	ereturn local depvar "``dep''"
42 | 	ereturn display
43 | end
44 | // test the program
45 | clear
46 | set more off
47 | set obs 1000
48 | // generate fake data
49 | gen z=rnormal()
50 | gen u=rnormal()
51 | gen x1=z+rnormal()+u
52 | gen x2=z+0.5*rnormal()
53 | gen y=2+x1+x2+u
54 | // compare it with ivregress commmand
55 | ivregress 2sls y (x1=z) x2
56 | twosls y, endo(x1) instru(z) control(x2)
57 | 


--------------------------------------------------------------------------------
/code_in_notes/uniform.c:
--------------------------------------------------------------------------------
 1 | // file: uniform.c
 2 | #include<stdio.h>
 3 | #include<stdlib.h> // 使用标准库<stdlib.h>，包含rand()
 4 | int main(int argc, char const *argv[]) {
 5 |   // 打印出rand()所生成的最大整数
 6 |   printf("%d\n",RAND_MAX);
 7 |   // 设置seed
 8 |   srand(505);
 9 |   // 生成(0,1)上的10个随机数
10 |   int i;
11 |   for (i=0; i<5; ++i){
12 |     double x=(double)rand()/RAND_MAX;
13 |     printf("%f  ",x);
14 |   }
15 |   printf("\n");
16 |   // 如果每次都设置seed生成(0,1)上的5个随机数
17 |   //那么每次生成的随机数都相同
18 |   for (i=0; i<5; ++i){
19 |     srand(505);
20 |     double x=(double)rand()/RAND_MAX;
21 |     printf("%f  ",x);
22 |   }
23 |   printf("\n");
24 |   return 0;
25 | }
26 | 


--------------------------------------------------------------------------------
/code_in_notes/uniform.do:
--------------------------------------------------------------------------------
 1 | // file: uniform.do
 2 | // 关闭--more--
 3 | set more off
 4 | // 清除工作区内所有数据
 5 | clear
 6 | // 设置样本量
 7 | set obs 100
 8 | // 设置seed
 9 | set seed 505
10 | // 产生随机数
11 | gen x=runiform()
12 | 


--------------------------------------------------------------------------------
/code_in_notes/uniform.py:
--------------------------------------------------------------------------------
 1 | #!/usr/bin/python3
 2 | ## file: uniform.py
 3 | 
 4 | # 导入random包
 5 | import random as rd
 6 | # 设置seed
 7 | rd.seed(505)
 8 | # 获取5个均匀分布随机数
 9 | x=[rd.random() for i in range(5)]
10 | print(x)
11 | # 导入numpy中的random包
12 | import numpy.random as nprd
13 | # 设置seed
14 | nprd.seed(505)
15 | # 获取5个均匀分布随机数
16 | x=nprd.random(5)
17 | print(x)
18 | 


--------------------------------------------------------------------------------
/code_in_notes/zipf_law.do:
--------------------------------------------------------------------------------
 1 | // zipf_law.do
 2 | clear
 3 | use datasets/citydata.dta
 4 | keep if Year==2011
 5 | sort v87
 6 | gen rank=_N-_n+1
 7 | gen log_rank=log10(rank)
 8 | gen log_pop=log10(v87*10000) // 数据的单位为万人
 9 | twoway (scatter log_pop log_rank if _n<_N-5) (scatter log_pop log_rank if _n>=_N-5, mlabel(City)), legend(off) xtitle("城市大小排序的对数（从大到小）") ytitle("人口的对数")
10 | graph export zipf_law.pdf, replace
11 | 


--------------------------------------------------------------------------------
/notebook_julia/Julia.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# Julia的安装\n",
  8 |     "Julia是一个开源的数值计算软件，由于具有JIT等特性，所以具有非常高的性能。我们可以从Julia官网：https://julialang.org 下载和安装。\n",
  9 |     "Julia的界面非常简单，不适合编写程序，因而我们一般通过配置Atom, sublime等编辑器写Julia程序。此外，通过安装Jupyter，再在Julia中安装IJulia也可以使用Jupyter调用Julia。安装IJulia的方法很简单，只需要在Julia的命令界面数据「Pkg.add(\"IJulia\")」即可，其中「Pkg.add()」即安装Julia扩展包的命令。\n",
 10 |     "为了展示方便，我们仍然推荐使用Jupyter作为学习工具。比如此文档就是使用Jupyter写作。\n",
 11 |     "# 使用Julia生成随机数\n",
 12 |     "在Julia中，可以使用rand()函数生成随机数。最基本的是生成一个在$(0,1)$区间内的均匀分布的随机数，使用此均匀分布随机数，给定任意的分布函数$F$，可以生成服从$F$的随机数。"
 13 |    ]
 14 |   },
 15 |   {
 16 |    "cell_type": "code",
 17 |    "execution_count": 2,
 18 |    "metadata": {},
 19 |    "outputs": [
 20 |     {
 21 |      "name": "stdout",
 22 |      "output_type": "stream",
 23 |      "text": [
 24 |       "一个(0,1)区间内的随机数：0.37548057506738663\n",
 25 |       "20个(0,1)区间内的随机数：\n",
 26 |       "[0.719472, 0.447485, 0.101696, 0.166868, 0.042199, 0.29615, 0.957232, 0.688239, 0.583882, 0.30275, 0.718666, 0.945527, 0.150395, 0.650269, 0.811649, 0.770101, 0.681383, 0.066861, 0.0560345, 0.760834]"
 27 |      ]
 28 |     }
 29 |    ],
 30 |    "source": [
 31 |     "## 生成一个x~Uniform(0,1)\n",
 32 |     "x=rand()\n",
 33 |     "print(\"一个(0,1)区间内的随机数：\",x,\"\\n\")\n",
 34 |     "\n",
 35 |     "## 生成20个z~Uniform(0,1)\n",
 36 |     "z=rand(20)\n",
 37 |     "print(\"20个(0,1)区间内的随机数：\",\"\\n\")\n",
 38 |     "print(z)"
 39 |    ]
 40 |   },
 41 |   {
 42 |    "cell_type": "markdown",
 43 |    "metadata": {},
 44 |    "source": [
 45 |     "如果我们需要生成一个服从分布函数$F: R\\rightarrow [0,1]$的随机数，那么只要首先生成一个$(0,1)$的随机数$u$，并令$x=F^{-1}(u)$，那么新生成的$x$即服从$F$的分布。比如，指数分布的分布函数为$1-e^{-\\frac{1}{b}\\cdot x}$，其中b为一个参数，因而我们可以使用$x=-b\\cdot \\ln(u)$来生成服从指数分布的随机数。"
 46 |    ]
 47 |   },
 48 |   {
 49 |    "cell_type": "code",
 50 |    "execution_count": 5,
 51 |    "metadata": {
 52 |     "scrolled": true
 53 |    },
 54 |    "outputs": [
 55 |     {
 56 |      "name": "stdout",
 57 |      "output_type": "stream",
 58 |      "text": [
 59 |       "20个服从指数分布F(x)=1-exp{-(1/b)*x}的随机数：\n",
 60 |       "[2.58645, 11.1848, 0.918512, 0.543136, 3.53971, 0.259657, 1.99849, 0.350091, 3.09114, 0.165935, 0.0657694, 0.949447, 9.25605, 0.393429, 10.0648, 1.87895, 2.65323, 6.0845, 6.48842, 2.73542]"
 61 |      ]
 62 |     }
 63 |    ],
 64 |    "source": [
 65 |     "## 设定参数\n",
 66 |     "b=3\n",
 67 |     "\n",
 68 |     "## 生成20个x~F(x)=1-exp{-(1/b)*x}\n",
 69 |     "x=-1*log.(rand(20))*b\n",
 70 |     "print(\"20个服从指数分布F(x)=1-exp{-(1/b)*x}的随机数：\\n\")\n",
 71 |     "print(x)"
 72 |    ]
 73 |   },
 74 |   {
 75 |    "cell_type": "markdown",
 76 |    "metadata": {},
 77 |    "source": [
 78 |     "我们可以使用经验分布函数（Empirical distribution function）与理论的分布函数比较，来判断我们生成的随机数是否满足某一分布。经验分布函数的定义为：$\\hat{F}(x)=\\frac{1}{N}\\cdot \\sum_{i=1}^N 1\\{X_i \\leq x\\}$，也就是给定一个$x$，其经验分布函数的值为样本中小于等于$x$的比例，比如："
 79 |    ]
 80 |   },
 81 |   {
 82 |    "cell_type": "code",
 83 |    "execution_count": 20,
 84 |    "metadata": {},
 85 |    "outputs": [
 86 |     {
 87 |      "name": "stdout",
 88 |      "output_type": "stream",
 89 |      "text": [
 90 |       " x  | 分布函数 | 经验分布函数| 差的绝对值\n",
 91 |       "0.1 |0.0327838995179941 | 0.035  | 0.002216100482005906 \n",
 92 |       "0.3 |0.09516258196404037 | 0.1  | 0.004837418035959634 \n",
 93 |       "0.5 |0.15351827510938598 | 0.185  | 0.031481724890614016 \n",
 94 |       "0.7 |0.20811043366321835 | 0.255  | 0.04688956633678165 \n",
 95 |       "0.9 |0.2591817793182821 | 0.295  | 0.03581822068171786 \n",
 96 |       "1.1 |0.3069593799135585 | 0.325  | 0.018040620086441528 \n",
 97 |       "1.3 |0.3516556589984903 | 0.4  | 0.04834434100150975 \n",
 98 |       "1.5 |0.3934693402873666 | 0.455  | 0.06153065971263344 \n",
 99 |       "1.7 |0.43258633120299617 | 0.495  | 0.06241366879700383 \n",
100 |       "1.9 |0.46918054943798604 | 0.54  | 0.070819450562014 \n",
101 |       "2.1 |0.5034146962085905 | 0.575  | 0.07158530379140948 \n",
102 |       "2.3 |0.5354409796390884 | 0.625  | 0.08955902036091157 \n",
103 |       "2.5 |0.5654017914929217 | 0.655  | 0.08959820850707834 \n",
104 |       "2.7 |0.5934303402594009 | 0.68  | 0.08656965974059916 \n",
105 |       "2.9 |0.6196512434107414 | 0.715  | 0.09534875658925857 \n",
106 |       "3.1 |0.6441810814626581 | 0.735  | 0.09081891853734192 \n",
107 |       "3.3 |0.6671289163019204 | 0.745  | 0.0778710836980796 \n",
108 |       "3.5 |0.6885967760854023 | 0.76  | 0.07140322391459775 \n",
109 |       "3.7 |0.708680108866529 | 0.77  | 0.06131989113347103 \n",
110 |       "3.9 |0.7274682069659874 | 0.785  | 0.05753179303401268 \n",
111 |       "4.1 |0.7450446039734899 | 0.795  | 0.04995539602651011 \n",
112 |       "4.3 |0.7614874461456975 | 0.8  | 0.03851255385430252 \n",
113 |       "4.5 |0.7768698398515702 | 0.81  | 0.033130160148429844 \n",
114 |       "4.7 |0.7912601766099203 | 0.825  | 0.03373982339007964 \n",
115 |       "4.9 |0.8047224371643142 | 0.835  | 0.030277562835685723 \n",
116 |       "5.1 |0.8173164759472653 | 0.845  | 0.027683524052734665 \n",
117 |       "5.3 |0.8290982871984751 | 0.85  | 0.020901712801524863 \n",
118 |       "5.5 |0.8401202539203061 | 0.86  | 0.019879746079693894 \n",
119 |       "5.7 |0.8504313807773649 | 0.87  | 0.019568619222635086 \n",
120 |       "5.9 |0.8600775119756906 | 0.87  | 0.009922488024309395 \n",
121 |       "6.1 |0.8691015350902557 | 0.88  | 0.010898464909744332 \n",
122 |       "6.3 |0.877543571747018 | 0.895  | 0.017456428252981993 \n",
123 |       "6.5 |0.8854411560073123 | 0.895  | 0.009558843992687693 \n",
124 |       "6.7 |0.8928294012476933 | 0.9  | 0.007170598752306745 \n",
125 |       "6.9 |0.8997411562771962 | 0.9  | 0.0002588437228038254 \n",
126 |       "7.1 |0.9062071513861237 | 0.91  | 0.0037928486138762985 \n",
127 |       "7.3 |0.9122561349757057 | 0.91  | 0.002256134975705648 \n",
128 |       "7.5 |0.9179150013761012 | 0.92  | 0.0020849986238988816 \n",
129 |       "7.7 |0.9232089104210319 | 0.92  | 0.0032089104210318853 \n",
130 |       "7.9 |0.9281613993106868 | 0.92  | 0.008161399310686712 \n",
131 |       "8.1 |0.9327944872602503 | 0.925  | 0.007794487260250227 \n",
132 |       "8.3 |0.9371287733993328 | 0.925  | 0.012128773399332715 \n",
133 |       "8.5 |0.9411835283575701 | 0.94  | 0.001183528357570185 \n",
134 |       "8.7 |0.9449767799435927 | 0.94  | 0.004976779943592802 \n",
135 |       "8.9 |0.9485253932982992 | 0.945  | 0.003525393298299262 \n",
136 |       "9.1 |0.9518451458788036 | 0.955  | 0.0031548541211963155 \n",
137 |       "9.3 |0.9549507976064422 | 0.955  | 4.92023935577679e-5 \n",
138 |       "9.5 |0.9578561564907236 | 0.955  | 0.0028561564907236825 \n",
139 |       "9.7 |0.9605741400209925 | 0.96  | 0.0005741400209925418 \n",
140 |       "9.9 |0.96311683259876 | 0.96  | 0.0031168325987600554 \n",
141 |       "Mean absolute bias:0.03123553671578694"
142 |      ]
143 |     }
144 |    ],
145 |    "source": [
146 |     "## 设定参数\n",
147 |     "b=3\n",
148 |     "\n",
149 |     "## 生成200个x~F(x)=1-exp{-(1/b)*x}\n",
150 |     "x=-1*log.(rand(200))*b\n",
151 |     "\n",
152 |     "## 给定一些点，在这些点上计算分布函数和经验分布函数\n",
153 |     "x_eval=[i for i in 0.1:0.2:9.9] #0.1,0.3,...,9.9\n",
154 |     "\n",
155 |     "## 计算理论的分布函数\n",
156 |     "F=1-exp.(-1/b.*x_eval)\n",
157 |     "\n",
158 |     "## 给定z计算经验分布函数\n",
159 |     "function empirical_F(x,z::Float64)::Float64\n",
160 |     "    return mean(x.<=z)\n",
161 |     "end\n",
162 |     "\n",
163 |     "## 计算经验分布函数\n",
164 |     "Fhat=[empirical_F(x,z) for z in x_eval]\n",
165 |     "\n",
166 |     "## 计算经验分布函数与真实的分布函数之间的绝对差异\n",
167 |     "bias=mean(abs.(Fhat-F))\n",
168 |     "## 打印两个分布函数及其绝对差异，以及平均的绝对差异\n",
169 |     "print(\" x  | 分布函数 | 经验分布函数| 差的绝对值\\n\")\n",
170 |     "for i in 1:1:length(x_eval)\n",
171 |     "    print(\"$(x_eval[i]) |$(F[i]) | $(Fhat[i])  | $(abs(F[i]-Fhat[i])) \\n\")\n",
172 |     "end\n",
173 |     "print(\"Mean absolute bias:\",bias)"
174 |    ]
175 |   },
176 |   {
177 |    "cell_type": "code",
178 |    "execution_count": null,
179 |    "metadata": {
180 |     "collapsed": true
181 |    },
182 |    "outputs": [],
183 |    "source": []
184 |   }
185 |  ],
186 |  "metadata": {
187 |   "kernelspec": {
188 |    "display_name": "Julia 0.6.0",
189 |    "language": "julia",
190 |    "name": "julia-0.6"
191 |   },
192 |   "language_info": {
193 |    "file_extension": ".jl",
194 |    "mimetype": "application/julia",
195 |    "name": "julia",
196 |    "version": "0.6.0"
197 |   },
198 |   "latex_envs": {
199 |    "LaTeX_envs_menu_present": true,
200 |    "autocomplete": true,
201 |    "bibliofile": "biblio.bib",
202 |    "cite_by": "apalike",
203 |    "current_citInitial": 1,
204 |    "eqLabelWithNumbers": true,
205 |    "eqNumInitial": 1,
206 |    "hotkeys": {
207 |     "equation": "Ctrl-E",
208 |     "itemize": "Ctrl-I"
209 |    },
210 |    "labels_anchors": false,
211 |    "latex_user_defs": false,
212 |    "report_style_numbering": false,
213 |    "user_envs_cfg": false
214 |   }
215 |  },
216 |  "nbformat": 4,
217 |  "nbformat_minor": 2
218 | }
219 | 


--------------------------------------------------------------------------------
/notebook_python/Poisson_Process.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# 生成泊松过程\n",
  8 |     "算法：首先生成一系列的指数分布，假设：$x_i\\sim E(0,1/\\lambda),i=0,1,...$，那么给定时间$t$，泊松分布可以由以下过程生成：$$ N(t)=\\arg \\min_t \\left\\{ \\sum _{i=0} ^{\\infty} x_i \\leq t \\right\\}$$"
  9 |    ]
 10 |   },
 11 |   {
 12 |    "cell_type": "code",
 13 |    "execution_count": 1,
 14 |    "metadata": {},
 15 |    "outputs": [],
 16 |    "source": [
 17 |     "import numpy as np\n",
 18 |     "import numpy.random as nprd\n",
 19 |     "\n",
 20 |     "## 设定参数\n",
 21 |     "b=1.0/100 #指数分布参数,一个小时平均到达100次\n",
 22 |     "Nexp=2000 #生成足够多的指数分布\n",
 23 |     "\n",
 24 |     "## 生成N个x~F(x)=1-exp{-(1/b)*x}\n",
 25 |     "X=-b*np.log(nprd.random(Nexp))\n",
 26 |     "S=[]\n",
 27 |     "s=0\n",
 28 |     "# 产生累积和\n",
 29 |     "for x in X:\n",
 30 |     "    s=s+x\n",
 31 |     "    S.append(s)\n",
 32 |     "\n",
 33 |     "## 给定一些时间点，比如从第一分钟到敌五分钟，在这些点上计算到达的个数\n",
 34 |     "t=np.linspace(0.0,5.0/60,500) #0.1,0.3,...,9.9\n",
 35 |     "N=np.zeros(len(t))\n",
 36 |     "i=0\n",
 37 |     "for tt in range(len(t)):\n",
 38 |     "    while t[tt]>=S[i]:\n",
 39 |     "        i=i+1\n",
 40 |     "    N[tt]=i\n"
 41 |    ]
 42 |   },
 43 |   {
 44 |    "cell_type": "code",
 45 |    "execution_count": 2,
 46 |    "metadata": {},
 47 |    "outputs": [
 48 |     {
 49 |      "data": {
 50 |       "image/png": 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AAAMxGgkw6JoAAwAYCCtg0D0BBgAwEAIMuifAAAAGQoBB9wQYAMBACDDongADABiItRsxA90RYAAAA2EFDLonwAAABsI29NA9AQYAMBBWwKB7AgwAYABqFWAwDwQYAMAAPP74OMIEGHRLgAEADEDTjI8CDLolwAAABkCAwXwQYAAAAyDAYD4IMACAAVgLMDdihm4JMACAARiNxkcrYNAtAQYAMAAuQYT5IMAAAAZAgMF8EGAAAAMgwGA+CDAAgAEQYDAfBBgAwAAIMJgPAgwAYAAEGMwHAQYAMAC2oYf5IMAAAAbAjZhhPggwAIABaJqklGTLlq4ngWETYAAAA9A048sPS+l6Ehg2AQYAMABrAQZ0S4ABAAyAAIP5sLnrAQAAhuy++5K/+Zuk1tm+zl13CTCYBwIMAKBDV1+d/NZvtfNar3hFO68DTCbAAAA69PDDybZtyUc+MvvXOumk2b8G8OwEGABAh5omOfbY5EUv6noSoA024QAA6JDNMWBYBBgAQIcEGAyLAAMA6JAAg2ERYAAAHRqNBBgMiQADAOiQFTAYFgEGANChpkmWl7ueAmiLAAMA6JAVMBgWAQYA0CEBBsMiwAAAOlKrAIOhEWAAAB15/PFxhAkwGA4BBgDQkaYZHwUYDIcAAwDoiACD4RFgAAAdGY3GRwEGwyHAAAA6YgUMhkeAAQB0ZC3A3IgZhkOAAQB0xAoYDI8AAwDoiACD4RFgAAAdEWAwPAIMAKAjAgyGR4ABAHREgMHwCDAAgI4IMBgeAQYA0BE3YobhEWAAAB2xAgbDI8AAADrSNEkpydJS15MAbRFgAAAdaZrx6lcpXU8CtEWAAQB0ZC3AgOEQYAAAHRFgMDwCDACgIwIMhkeAAQB0RIDB8AgwAICOCDAYHgEGANCR0UiAwdAIMACAjlgBg+ERYAAAHWmaZHm56ymANgkwAICOWAGD4RFgAAAdEWAwPAIMAKAjAgyGR4ABAHREgMHwCDAAgA7Uaht6GKINB1gpZVMp5TOllL+c5UAAAEMwGo2PAgyG5bmsgL0lyZ2zGgQAYEgEGAzT5o08qZSyNclrk1yT5O0znQgAYIO+9rXkgx9MHn+860meu699bXx0HzAYlg0FWJLrkrwjyTGTnlBK2ZFkR5Js27btsAcDADiUP/mT5E1v6nqK71wpyamndj0F0KZDBlgp5dIk99dabyulvGLS82qtO5PsTJKVlZU6rQEBACZZW0W6++7k2GO7neU7sbTUz7mB79xGVsAuTPKjpZRLkiwnObaUcn2t9SdnOxoAwLNrmvHxpJOSLVu6nQVgIw65CUet9Z211q211pOTXJ7kb8UXADAPRqPkiCPGK0kAfeA+YABAbzXNeBOLUrqeBGBjNroJR5Kk1vp3Sf5uJpMAADxHTWMbd6BfrIABAL0lwIC+EWAAQG8JMKBvBBgA0FsCDOgbAQYA9JYAA/pGgAEAvSXAgL4RYABAb61tQw/QFwIMAOit0cgKGNAvAgwA6C2XIAJ9I8AAgN4SYEDfCDAAoLcEGNA3AgwA6C0BBvSNAAMAeqlWm3AA/SPAAIBeGo3GRwEG9IkAAwB6qWnGR/cBA/pEgAEAvbQWYFbAgD4RYABAL7kEEegjAQYA9JIVMKCPBBgA0EsCDOgjAQYA9JIAA/pIgAEAvSTAgD4SYABAL9mGHugjAQYA9JIVMKCPBBgA0EsCDOgjAQYA9JIAA/pIgAEAveRGzEAfCTAAoJesgAF9JMAAgF5qmmTTpmRpqetJADZOgAEAvdQ0Vr+A/hFgAEAvNY17gAH9I8AAgF6yAgb0kQADAHpJgAF9JMAAgF4SYEAfCTAAoJcEGNBHAgwA6KXRSIAB/SPAAIBesgIG9JEAAwB6yTb0QB8JMACgl6yAAX20uesBAGbthhuS3bu7ngKYtgcfFGBA/wgwYOFdeWXyjW90PQUwC+ec0/UEAM+NAAMWWq3j+PrFX0yuvrrraQCAofMZMGChjUbjo8uUAIB5IMCAhdY046MAAwDmgQADFpoAAwDmiQADFpoAAwDmiQADFpoAAwDmiQADFppNOACAeSLAgIVmBQwAmCcCDFhoAgwAmCcCDFhoawG2vNztHAAAiQADFpwVMABgnggwYKEJMABgnggwYKEJMABgnggwYKHZhh4AmCcCDFhoVsAAgHkiwICF1jTJpk3J0lLXkwAACDBgwTWN1S8AYH4IMGChCTAAYJ4IMGChNY2bMAMA80OAAQvNChgAME8EGLDQBBgAME8EGLDQRiMBBgDMDwEGLDQrYADAPBFgwEITYADAPBFgwEITYADAPBFgwEITYADAPBFgwEITYADAPBFgwEJzI2YAYJ4IMGCh2YYeAJgnAgxYWE8+mezbJ8AAgPkhwICFNRqNjwIMAJgXAgxYWE0zPgowAGBeCDBgYQkwAGDeCDBgYQkwAGDeCDBgYQkwAGDeCDBgYQkwAGDeCDBgYa3tguhGzADAvBBgwMKyAgYAzBsBBiwsAQYAzJtDBlgp5YWllFtKKXeWUvaUUt7SxmAAh0uAAQDzZvMGnrM/yVW11k+XUo5Jclsp5a9rrXfMeDaAwyLAAIB5c8gVsFrrP9daP33w548muTPJSbMeDOBwCTAAYN5sZAXsKaWUk5Ocl+QTM5kGWFhf+lLym7+Z7N/f3mt+5jPjowADAObFhgOslPJdSf40yVtrrV9b57/vSLIjSbZt2za1AYHF8Md/nLznPclxxyWltPe627cnRx3V3usBADybDQVYKWUp4/j6QK31Q+s9p9a6M8nOJFlZWalTmxBYCI89Nj4+9FByhP1XAYCB2sguiCXJ7yW5s9b6G7MfCVhETZM873niCwAYto38VejCJFck+eFSyq6DPy6Z8VzAgmkan8UCADjkJYi11o8mafETG8AiEmAAABtbAQM4bKORAAMAEGBAK5omWV7uegoAgG4JMKAVLkEEABBgQEsEGACAAANaIsAAAAQY0BIBBgAgwICWCDAAAAEGtESAAQAIMKAlAgwAQIABLRmN3AcMAECAAa2wAgYAIMCAFjzxRHLggAADABBgwMw1zfgowACAoRNgwMwJMACAMQEGzJwAAwAYE2DAzAkwAIAxAQbM3FqA2YYeABg6AQbMnBUwAIAxAQbM3Gg0PgowAGDoBBgwc1bAAADGBBgwcwIMAGBMgAEzJ8AAAMYEGDBzAgwAYEyAATNnG3oAgDEBBsycFTAAgDEBBsycFTAAgDEBBsxc04zjq5SuJwEA6JYAA2ZuNHL5IQBAIsCAFjSNAAMASAQY0AIBBgAwJsCAmRNgAABjAgyYubVNOAAAhk6AATNnBQwAYEyAATMnwAAAxgQYMHMCDABgTIABMyfAAADGBBgwc27EDAAwJsCAmbMCBgAwtrnrARbRhz+cXH9911PA/HjkEdvQAwAkAmwmfvu3k5tvTrZt63oSmA+nnpq84hVdTwEA0D0BNgOPPZasrCQf+1jXkwAAAPPEZ8BmwIYDAADAegTYDNhwAAAAWI8Am4GmseEAAADwTAJsBqyAAQAA6xFgMyDAAACA9QiwGRBgAADAegTYDAgwAABgPQJsyg4cSJ54QoABAADPJMCmrGnGRwEGAAA8nQCbstFofBRgAADA0wmwKbMCBgAATCLApmwtwNyIGQAAeDoBNmVWwAAAgEkE2JQJMAAAYBIBNmUCDAAAmESATZkAAwAAJhFgUybAAACASQTYlAkwAABgEgE2ZW7EDAAATCLApswKGAAAMIkAmzI3YgYAACYRYFNmBQwAAJhEgE1Z0yRbtiRH+J0FAACeRiZMWdNY/QIAANYnwKZMgAEAAJMIsCkTYAAAwCQCbMoEGAAAMIkAm7LRSIABAADrE2BTZgUMAACYRIBNWdO4CTMAALA+ATZlVsAAAIBJBNiUCTAAAGASATZlAgwAAJhEgE2ZAAMAACYRYFMmwAAAgEkE2JQJMAAAYBIBNkX79ycHDggwAABgfQJsippmfBRgAADAejYUYKWUV5dSPldK+Xwp5ednPVRfrQWYGzEDAADrOWSAlVI2JXlfktckOSPJj5dSzpj1YH1kBQwAAHg2G1kB257k87XWu2utjyf5oySvm+1Y/STAAACAZ7N5A885Kck93/L13iQXzGac2fiXf0muvHL2r/Poo+OjAAMAANazkQAr6zxWn/GkUnYk2ZEk27ZtO8yxpuvJJ5OHH27ntV75ymRlpZ3XAgAA+mUjAbY3yQu/5eutSe59+pNqrTuT7EySlZWVZwRal773e5N//MeupwAAAIZuI58B+1SSF5VSTimlbElyeZI/n+1YAAAAi+eQK2C11v2llJ9LcnOSTUneX2vdM/PJAAAAFsxGLkFMrfXGJDfOeBYAAICFtqEbMQMAAHD4BBgAAEBLBBgAAEBLBBgAAEBLBBgAAEBLBBgAAEBLBBgAAEBLBBgAAEBLBBgAAEBLBBgAAEBLBBgAAEBLBBgAAEBLBBgAAEBLBBgAAEBLBBgAAEBLSq11+ict5YEkX5r6iQ/f85M82PUQLCzvL2bJ+4tZ8v5ilry/mLV5fY/9m1rrCU9/cCYBNq9KKbfWWle6noPF5P3FLHl/MUveX8yS9xez1rf3mEsQAQAAWiLAAAAAWjK0ANvZ9QAsNO8vZsn7i1ny/mKWvL+YtV69xwb1GTAAAIAuDW0FDAAAoDODCLBSyqtLKZ8rpXy+lPLzXc/DYimlvL+Ucn8pZXfXs7B4SikvLKXcUkq5s5Syp5Tylq5nYnGUUpZLKZ8spXz24Pvr3V3PxOIppWwqpXymlPKXXc/CYimlfLGUslpK2VVKubXreTZq4S9BLKVsSvJ/k/z7JHuTfCrJj9da7+h0MBZGKeXlSb6e5H/UWs/qeh4WSynlBUleUGv9dCnlmCS3JXm9/4cxDaWUkuToWuvXSylLST6a5C211n/seDQWSCnl7UlWkhxba72063lYHKWULyZZqbXO4z3AJhrCCtj2JJ+vtd5da308yR8leV3HM7FAaq3/J8lXup6DxVRr/eda66cP/vzRJHcmOanbqVgUdezrB79cOvhjsf9lllaVUrYmeW2S/9b1LDAvhhBgJyW551u+3ht/eQF6qJRycpLzknyi41FYIAcvD9uV5P4kf11r9f5imq5L8o4kT3Y8B4upJvmrUsptpZQdXQ+zUUMIsLLOY/51D+iVUsp3JfnTJG+ttX6t63lYHLXWA7XWc5NsTbK9lOJSaqailHJpkvtrrbd1PQsL68Ja6/lJXpPkPx38WMjcG0KA7U3ywm/5emuSezuaBeA5O/jZnD9N8oFa64e6nofFVGt9OMnfJXl1t5OwQC5M8qMHP6fzR0l+uJRyfbcjsUhqrfcePN6f5H9l/NGjuTeEAPtUkheVUk4ppWxJcnmSP+94JoANObhJwu8lubPW+htdz8NiKaWcUEo57uDPj0xycZK7Oh2KhVFrfWetdWut9eSM//71t7XWn+x4LBZEKeXog5tTpZRydJL/kKQXO1IvfIDVWvcn+bkkN2f84fU/qbXu6XYqFkkp5YNJPp7kB0ope0spb+x6JhbKhUmuyPhfjncd/HFJ10OxMF6Q5JZSyu0Z/4PlX9dabRUO9MG/TvLRUspnk3wyyf+utd7U8UwbsvDb0AMAAMyLhV8BAwAAmBcCDAAAoCUCDAAAoCUCDAAAoCUCDAAAoCUCDAAAoCUCDAAAoCUCDAAAoCX/H7zCL1244ou/AAAAAElFTkSuQmCC",
 51 |       "text/plain": [
 52 |        "<Figure size 1080x576 with 1 Axes>"
 53 |       ]
 54 |      },
 55 |      "metadata": {
 56 |       "needs_background": "light"
 57 |      },
 58 |      "output_type": "display_data"
 59 |     }
 60 |    ],
 61 |    "source": [
 62 |     "## 导入matplotlib\n",
 63 |     "import matplotlib.pyplot as plt \n",
 64 |     "## 使图形直接插入到jupyter中\n",
 65 |     "%matplotlib inline\n",
 66 |     "# 设定图像大小\n",
 67 |     "plt.rcParams['figure.figsize'] = (15.0, 8.0)\n",
 68 |     "\n",
 69 |     "t_plot=[tt*60 for tt in t]\n",
 70 |     "plt.plot(t_plot,N,label=r'$Poisson Process$',color='blue')\n",
 71 |     "plt.legend(loc='upper left', frameon=True)\n",
 72 |     "plt.show() ## 画图"
 73 |    ]
 74 |   },
 75 |   {
 76 |    "cell_type": "markdown",
 77 |    "metadata": {},
 78 |    "source": [
 79 |     "# 复合泊松过程\n",
 80 |     "算法：给定$N(t)$为一个泊松过程，现在假设$Z_j\\sim N(0,1)$，那么复合泊松过程为：$$M(t)=\\sum _{j=1} ^{N(t)} Z_j$$"
 81 |    ]
 82 |   },
 83 |   {
 84 |    "cell_type": "code",
 85 |    "execution_count": 3,
 86 |    "metadata": {},
 87 |    "outputs": [
 88 |     {
 89 |      "data": {
 90 |       "image/png": 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",
 91 |       "text/plain": [
 92 |        "<Figure size 1080x576 with 1 Axes>"
 93 |       ]
 94 |      },
 95 |      "metadata": {
 96 |       "needs_background": "light"
 97 |      },
 98 |      "output_type": "display_data"
 99 |     }
100 |    ],
101 |    "source": [
102 |     "# 生成一系列正态分布\n",
103 |     "Z=nprd.normal(0,1,int(N[-1]))\n",
104 |     "SZ=[]\n",
105 |     "s=0\n",
106 |     "for z in Z:\n",
107 |     "    s=s+z\n",
108 |     "    SZ.append(s)\n",
109 |     "\n",
110 |     "# 生成复合泊松过程\n",
111 |     "M=[]\n",
112 |     "for n in N:\n",
113 |     "    if int(n)==0:\n",
114 |     "        M.append(0)\n",
115 |     "    else:\n",
116 |     "        M.append(SZ[int(n)-1])\n",
117 |     "M=np.array(M)\n",
118 |     "\n",
119 |     "## 导入matplotlib\n",
120 |     "import matplotlib.pyplot as plt \n",
121 |     "## 使图形直接插入到jupyter中\n",
122 |     "%matplotlib inline\n",
123 |     "# 设定图像大小\n",
124 |     "plt.rcParams['figure.figsize'] = (15.0, 8.0)\n",
125 |     "\n",
126 |     "t_plot=[tt*60 for tt in t]\n",
127 |     "plt.plot(t_plot,M,label=r'$Compound Poisson Process$',color='blue')\n",
128 |     "plt.legend(loc='upper left', frameon=True)\n",
129 |     "plt.show() ## 画图"
130 |    ]
131 |   }
132 |  ],
133 |  "metadata": {
134 |   "kernelspec": {
135 |    "display_name": "Anaconda",
136 |    "language": "python",
137 |    "name": "anaconda"
138 |   },
139 |   "language_info": {
140 |    "codemirror_mode": {
141 |     "name": "ipython",
142 |     "version": 3
143 |    },
144 |    "file_extension": ".py",
145 |    "mimetype": "text/x-python",
146 |    "name": "python",
147 |    "nbconvert_exporter": "python",
148 |    "pygments_lexer": "ipython3",
149 |    "version": "3.9.12"
150 |   }
151 |  },
152 |  "nbformat": 4,
153 |  "nbformat_minor": 2
154 | }
155 | 


--------------------------------------------------------------------------------
/notebook_python/Random_number.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "metadata": {},
  7 |    "outputs": [
  8 |     {
  9 |      "data": {
 10 |       "image/png": 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",
 11 |       "text/plain": [
 12 |        "<Figure size 576x360 with 1 Axes>"
 13 |       ]
 14 |      },
 15 |      "metadata": {
 16 |       "needs_background": "light"
 17 |      },
 18 |      "output_type": "display_data"
 19 |     }
 20 |    ],
 21 |    "source": [
 22 |     "import numpy as np\n",
 23 |     "import numpy.random as nprd\n",
 24 |     "# 获取序贯的1000个均匀分布随机数\n",
 25 |     "x = nprd.random(1000)\n",
 26 |     "# 将1000个均匀分布随机数按照奇偶数分成两个序列x0 和x1\n",
 27 |     "x0 = np.array([x[i] for i in range(1000) if i % 2 == 0])\n",
 28 |     "x1 = np.array([x[i] for i in range(1000) if i % 2 == 1])\n",
 29 |     "# 画图\n",
 30 |     "import matplotlib.pyplot as plt\n",
 31 |     "# 设定图像大小\n",
 32 |     "plt.rcParams['figure.figsize'] = (8.0, 5.0)\n",
 33 |     "plt.scatter(x0, x1, color='blue')  ## 画出散点图\n",
 34 |     "plt.savefig(\"check_random_py.pdf\")\n"
 35 |    ]
 36 |   },
 37 |   {
 38 |    "cell_type": "code",
 39 |    "execution_count": 2,
 40 |    "metadata": {},
 41 |    "outputs": [
 42 |     {
 43 |      "name": "stdout",
 44 |      "output_type": "stream",
 45 |      "text": [
 46 |       "2.109375\n"
 47 |      ]
 48 |     },
 49 |     {
 50 |      "data": {
 51 |       "image/png": 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",
 52 |       "text/plain": [
 53 |        "<Figure size 576x360 with 1 Axes>"
 54 |       ]
 55 |      },
 56 |      "metadata": {
 57 |       "needs_background": "light"
 58 |      },
 59 |      "output_type": "display_data"
 60 |     }
 61 |    ],
 62 |    "source": [
 63 |     "#!/usr/bin/python3\n",
 64 |     "## file: rejection_beta.py\n",
 65 |     "import numpy as np\n",
 66 |     "import numpy.random as nprd\n",
 67 |     "import scipy.special as scisp\n",
 68 |     "# 设定参数\n",
 69 |     "alpha = 4\n",
 70 |     "beta = 2\n",
 71 |     "# beta分布密度函数\n",
 72 |     "f=lambda x: 1/scisp.beta(alpha,beta)* \\\n",
 73 |     "    x**(alpha-1) * (1-x)**(beta-1)\n",
 74 |     "# 计算密度函数最大值\n",
 75 |     "M = f((1 - alpha) / (2 - alpha - beta))\n",
 76 |     "print(M)\n",
 77 |     "# 随机抽两个均匀分布，一个为(0,1)，一个为(0,M)，抽500个\n",
 78 |     "N = 500\n",
 79 |     "x = nprd.random(N)\n",
 80 |     "u = nprd.random(N) * M\n",
 81 |     "# 挑出使得u<beta密度函数的x\n",
 82 |     "accepted = [i for i in range(N) if u[i] <= f(x[i])]\n",
 83 |     "rand_beta = x[accepted]  #生成的Beta分布随机数\n",
 84 |     "rand_U_selected = u[accepted]\n",
 85 |     "# 画图\n",
 86 |     "import matplotlib.pyplot as plt\n",
 87 |     "# 设定图像大小和坐标范围\n",
 88 |     "plt.rcParams['figure.figsize'] = (8.0, 5.0)\n",
 89 |     "plt.xlim(0, 1)\n",
 90 |     "plt.ylim(0, M + 0.1)\n",
 91 |     "# 横线和竖线\n",
 92 |     "x_grid = np.linspace(0, 1, 100)  #(0,1)均匀的100个点\n",
 93 |     "y_M = np.ones(100) * M\n",
 94 |     "beta_dens = f(x_grid)\n",
 95 |     "y1 = np.linspace(0, f(0.4), 20)\n",
 96 |     "y2 = np.linspace(f(0.4), M, 20)\n",
 97 |     "x_hline = np.ones(20) * 0.4\n",
 98 |     "plt.xlabel(r'$X$')\n",
 99 |     "plt.ylabel(r'$U$')\n",
100 |     "plt.title('Sampling from Beta dist.')  # 标题\n",
101 |     "## 画出散点图\n",
102 |     "plt.scatter(x, u, color='blue', s=0.8)\n",
103 |     "plt.scatter(rand_beta, rand_U_selected, color='black', s=0.8)\n",
104 |     "plt.plot(x_grid, y_M, color='red')  ## 最大值\n",
105 |     "plt.plot(x_grid, beta_dens, color='orange')  ## 密度函数\n",
106 |     "plt.plot(x_hline, y1, color='grey')  ## 接受区域\n",
107 |     "plt.text(0.42, 0.3, \"Acceptance\", fontsize=15, horizontalalignment=\"left\")\n",
108 |     "plt.plot(x_hline, y2, color='pink')  ## 拒绝区域\n",
109 |     "plt.text(0.38, 1.5, \"Rejection\", fontsize=15, horizontalalignment=\"right\")\n",
110 |     "plt.savefig(\"rejection_beta.pdf\")\n"
111 |    ]
112 |   }
113 |  ],
114 |  "metadata": {
115 |   "kernelspec": {
116 |    "display_name": "Anaconda",
117 |    "language": "python",
118 |    "name": "anaconda"
119 |   },
120 |   "language_info": {
121 |    "codemirror_mode": {
122 |     "name": "ipython",
123 |     "version": 3
124 |    },
125 |    "file_extension": ".py",
126 |    "mimetype": "text/x-python",
127 |    "name": "python",
128 |    "nbconvert_exporter": "python",
129 |    "pygments_lexer": "ipython3",
130 |    "version": "3.9.12"
131 |   },
132 |   "orig_nbformat": 4,
133 |   "vscode": {
134 |    "interpreter": {
135 |     "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"
136 |    }
137 |   }
138 |  },
139 |  "nbformat": 4,
140 |  "nbformat_minor": 2
141 | }
142 | 


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/notebook_python/estimation.ipynb:
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  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# Beta分布的矩估计\n",
  8 |     "如果$x_i \\sim Beta(\\alpha, \\beta)$，由于$E(x_i)=\\frac{\\alpha}{\\alpha + \\beta}$，而$E(x_i^2)=\\frac{\\alpha ^2}{(\\alpha + \\beta)^2}+\\frac{\\alpha \\beta}{(\\alpha + \\beta)^2 (\\alpha+\\beta+1)}$，从而我们的矩估计即联立：$$\\frac{\\hat{\\alpha}}{\\hat{\\alpha} + \\hat{\\beta}}=\\bar{x}$$ $$\\frac{\\hat{\\alpha} ^2}{(\\hat{\\alpha} + \\hat{\\beta})^2}+\\frac{\\hat{\\alpha} \\hat{\\beta}}{(\\hat{\\alpha} + \\hat{\\beta})^2 (\\hat{\\alpha}+\\hat{\\beta}+1)}=\\overline{x^{2}}$$ 即可得到矩估计。在这里，我们将联立方程问题转化为一个最优化问题，即最小化： $$\\min_{\\hat{\\alpha},\\hat{\\beta}}\\left[\\frac{\\hat{\\alpha}}{\\hat{\\alpha} + \\hat{\\beta}}-\\bar{x} \\right]^2+\\left[\\frac{\\hat{\\alpha} ^2}{(\\hat{\\alpha} + \\hat{\\beta})^2}+\\frac{\\hat{\\alpha} \\hat{\\beta}}{(\\hat{\\alpha} + \\hat{\\beta})^2 (\\hat{\\alpha}+\\hat{\\beta}+1)}-\\overline{x^{2}}\\right]^2$$\n",
  9 |     "我们将会重复抽样、估计M=500次，并根据这500次的结果计算矩估计量的偏差（bias）、标准误(standard error)以及均方误差（mean sqrared error）。"
 10 |    ]
 11 |   },
 12 |   {
 13 |    "cell_type": "code",
 14 |    "execution_count": 1,
 15 |    "metadata": {},
 16 |    "outputs": [
 17 |     {
 18 |      "name": "stdout",
 19 |      "output_type": "stream",
 20 |      "text": [
 21 |       "Bias =  [0.04160227 0.0142872 ]\n",
 22 |       "s.e. =  [0.33877233 0.10751308]\n",
 23 |       "RMSE =  [0.34131722 0.10845823]\n"
 24 |      ]
 25 |     }
 26 |    ],
 27 |    "source": [
 28 |     "import numpy as np\n",
 29 |     "from numpy import random as nprd\n",
 30 |     "from scipy.optimize import minimize\n",
 31 |     "import scipy as sc\n",
 32 |     "\n",
 33 |     "def sampling(a,b,N):\n",
 34 |     "    x=nprd.beta(a,b,N)\n",
 35 |     "    return x\n",
 36 |     "\n",
 37 |     "def estimate(x):\n",
 38 |     "    meanx=np.mean(x)\n",
 39 |     "    x2=[xi**2 for xi in x]\n",
 40 |     "    meanx2=np.mean(x2)\n",
 41 |     "    def obj(theta):\n",
 42 |     "        return (theta[0]/(theta[0]+theta[1])-meanx)**2 + ((theta[0]/(theta[0]+theta[1]))**2+(theta[0]*theta[1])/((theta[0]+theta[1])**2*(theta[0]+theta[1]+1))-meanx2)**2\n",
 43 |     "    res=minimize(obj, np.array([1,1]), method='nelder-mead', options={'xtol': 1e-4, 'disp': False})\n",
 44 |     "    return res\n",
 45 |     "\n",
 46 |     "M=500 ## simulation times\n",
 47 |     "N=200 ## sample size\n",
 48 |     "a=3\n",
 49 |     "b=1 ## true value\n",
 50 |     "RESULT=np.zeros((M,2), np.float64)\n",
 51 |     "for m in range(M):\n",
 52 |     "    x=sampling(a,b,N)\n",
 53 |     "    res=estimate(x)\n",
 54 |     "    RESULT[m]=res.x\n",
 55 |     "\n",
 56 |     "MEAN_RESULT=np.average(RESULT, 0)\n",
 57 |     "BIAS=MEAN_RESULT-np.array([a,b])\n",
 58 |     "STD=np.std(RESULT, 0)\n",
 59 |     "MSE2=np.array([i**2 for i in STD])+np.array([i**2 for i in BIAS])\n",
 60 |     "MSE=np.array([np.sqrt(i) for i in MSE2])\n",
 61 |     "print(\"Bias = \", BIAS)\n",
 62 |     "print(\"s.e. = \", STD)\n",
 63 |     "print(\"RMSE = \", MSE)"
 64 |    ]
 65 |   },
 66 |   {
 67 |    "cell_type": "markdown",
 68 |    "metadata": {
 69 |     "collapsed": true
 70 |    },
 71 |    "source": [
 72 |     "# Beta分布的极大似然估计\n",
 73 |     "由于Beta分布的对数似然函数为$$\\ln \\left( \\alpha, \\beta | x \\right)=\\sum_{i=1}^N \\left[ -\\ln (Beta(\\alpha,\\beta))+(\\alpha-1) \\ln (x_i) + (\\beta-1)\\ln (1-x_i) \\right]$$\n",
 74 |     "最大化似然函数，或者最小化负的似然函数，即可得到极大似然估计。"
 75 |    ]
 76 |   },
 77 |   {
 78 |    "cell_type": "code",
 79 |    "execution_count": 2,
 80 |    "metadata": {},
 81 |    "outputs": [
 82 |     {
 83 |      "name": "stdout",
 84 |      "output_type": "stream",
 85 |      "text": [
 86 |       "Bias =  [0.04085049 0.00445378]\n",
 87 |       "s.e. =  [0.3179479  0.08854558]\n",
 88 |       "RMSE =  [0.32056143 0.08865752]\n"
 89 |      ]
 90 |     }
 91 |    ],
 92 |    "source": [
 93 |     "import numpy as np\n",
 94 |     "from numpy import random as nprd\n",
 95 |     "from scipy.optimize import minimize\n",
 96 |     "import scipy as sc\n",
 97 |     "\n",
 98 |     "def sampling(a,b,N):\n",
 99 |     "    x=nprd.beta(a,b,N)\n",
100 |     "    return x\n",
101 |     "    \n",
102 |     "def estimate(x):\n",
103 |     "    def log_likelihood(theta):\n",
104 |     "        likeli=np.array([-1*np.log(sc.special.beta(theta[0],theta[1]))+(theta[0]-1)*np.log(xi)+(theta[1]-1)*np.log(1-xi) for xi in x])\n",
105 |     "        return -1*np.mean(likeli)\n",
106 |     "    res=minimize(log_likelihood, np.array([1,1]), method='nelder-mead', options={'xtol': 1e-4, 'disp': False})\n",
107 |     "    return res\n",
108 |     "\n",
109 |     "M=500 ## simulation times\n",
110 |     "N=200 ## sample size\n",
111 |     "a=3\n",
112 |     "b=1 ## true value\n",
113 |     "RESULT=np.zeros((M,2), np.float64)\n",
114 |     "for m in range(M):\n",
115 |     "    x=sampling(a,b,N)\n",
116 |     "    res=estimate(x)\n",
117 |     "    RESULT[m]=res.x\n",
118 |     "\n",
119 |     "MEAN_RESULT=np.average(RESULT, 0)\n",
120 |     "BIAS=MEAN_RESULT-np.array([a,b])\n",
121 |     "STD=np.std(RESULT, 0)\n",
122 |     "MSE2=np.array([i**2 for i in STD])+np.array([i**2 for i in BIAS])\n",
123 |     "MSE=np.array([np.sqrt(i) for i in MSE2])\n",
124 |     "print(\"Bias = \", BIAS)\n",
125 |     "print(\"s.e. = \", STD)\n",
126 |     "print(\"RMSE = \", MSE)"
127 |    ]
128 |   },
129 |   {
130 |    "cell_type": "markdown",
131 |    "metadata": {},
132 |    "source": [
133 |     "通过比较，发现尽管Bias有大有效，但是极大似然估计的确比矩估计更有效。"
134 |    ]
135 |   },
136 |   {
137 |    "cell_type": "markdown",
138 |    "metadata": {},
139 |    "source": [
140 |     "# 区间估计\n",
141 |     "## 小样本正态总体\n",
142 |     "如果$x_i\\sim N\\left(  \\mu, \\sigma^2 \\right)$，那么$\\bar{x}\\sim N\\left(\\mu,\\frac{\\sigma^2}{N}\\right)$，或者，如果我们用样本方差替代总体方差，那么有：$$\\frac{\\bar{x}-\\mu}{\\sqrt{\\frac{s^2}{N}}}\\sim t(N-1)$$\n",
143 |     "因而，对于总体均值$\\mu$的95%置信水平的区间估计为$$\\left[\\bar{x}-t_{1-\\alpha}(N-1)\\sqrt{\\frac{s^2}{N}},\\bar{x}+t_{1-\\alpha}(N-1)\\sqrt{\\frac{s^2}{N}}\\right]$$\n",
144 |     "下面我们将重复1000次区间估计，理论上，在95%置信水平下，应该有950次区间估计包含真值，我们将看到这一结论是否成立。"
145 |    ]
146 |   },
147 |   {
148 |    "cell_type": "code",
149 |    "execution_count": 3,
150 |    "metadata": {},
151 |    "outputs": [
152 |     {
153 |      "name": "stdout",
154 |      "output_type": "stream",
155 |      "text": [
156 |       "The prob. of included= 0.942\n"
157 |      ]
158 |     }
159 |    ],
160 |    "source": [
161 |     "import numpy as np\n",
162 |     "from numpy import random as nprd\n",
163 |     "from scipy import special as func\n",
164 |     "\n",
165 |     "def sampling(mu, sigma2, N):\n",
166 |     "    x=nprd.normal(mu,np.sqrt(sigma2),N)\n",
167 |     "    return x\n",
168 |     "\n",
169 |     "## true value\n",
170 |     "mu=10\n",
171 |     "sigma2=30\n",
172 |     "N=10 # sample size\n",
173 |     "## iteration times\n",
174 |     "M=1000\n",
175 |     "## confidence level\n",
176 |     "alpha=0.05\n",
177 |     "## results\n",
178 |     "included=np.zeros(M)\n",
179 |     "for i in range(M):\n",
180 |     "    x=sampling(mu,sigma2,10)\n",
181 |     "    xmean=np.mean(x)\n",
182 |     "    xstd=np.std(x)\n",
183 |     "    lower=xmean-func.stdtrit(N-1,1-alpha/2)*xstd/np.sqrt(N)\n",
184 |     "    upper=xmean+func.stdtrit(N-1,1-alpha/2)*xstd/np.sqrt(N)\n",
185 |     "    # 如果包含真值\n",
186 |     "    if mu>=lower and mu<=upper:\n",
187 |     "        included[i]=1\n",
188 |     "print(\"The prob. of included=\",np.mean(included))"
189 |    ]
190 |   },
191 |   {
192 |    "cell_type": "markdown",
193 |    "metadata": {},
194 |    "source": [
195 |     "# 区间估计\n",
196 |     "## 大样本总体未知\n",
197 |     "如果$x_i\\sim \\left(  \\mu, \\sigma^2 \\right)$，那么当样本量足够大时，$\\bar{x}\\sim N\\left(\\mu,\\frac{\\sigma^2}{N}\\right)$，或者，如果我们用样本方差替代总体方差，那么当样本量足够大时，有：$$\\frac{\\bar{x}-\\mu}{\\sqrt{\\frac{s^2}{N}}}\\sim N\\left(0,1\\right)$$\n",
198 |     "下面我们将重复1000次区间估计，理论上，在95%置信水平下，应该有950次区间估计包含真值，我们将看到这一结论是否成立。"
199 |    ]
200 |   },
201 |   {
202 |    "cell_type": "code",
203 |    "execution_count": 4,
204 |    "metadata": {},
205 |    "outputs": [
206 |     {
207 |      "name": "stdout",
208 |      "output_type": "stream",
209 |      "text": [
210 |       "Sample size=10, the prob. of included= 0.93\n",
211 |       "Sample size=50, the prob. of included= 0.94\n",
212 |       "Sample size=100, the prob. of included= 0.94\n",
213 |       "Sample size=500, the prob. of included= 0.955\n",
214 |       "Sample size=1000, the prob. of included= 0.948\n"
215 |      ]
216 |     }
217 |    ],
218 |    "source": [
219 |     "import numpy as np\n",
220 |     "from numpy import random as nprd\n",
221 |     "from scipy import special as func\n",
222 |     "\n",
223 |     "def sampling(N):\n",
224 |     "    ## 产生一组样本，以0.5的概率为z+3，0.5的概率为z-3，其中z~N(0,1)，因而期望为0，方差为10\n",
225 |     "    d=nprd.rand(N)<0.5\n",
226 |     "    z=nprd.randn(N)\n",
227 |     "    x=np.array([z[i]+3 if d[i] else z[i]-3 for i in range(N)])\n",
228 |     "    return x\n",
229 |     "\n",
230 |     "## true value\n",
231 |     "N=[10,50,100,500,1000] # sample size\n",
232 |     "## iteration times\n",
233 |     "M=1000\n",
234 |     "## confidence level\n",
235 |     "alpha=0.05\n",
236 |     "for n in N:\n",
237 |     "    ## results\n",
238 |     "    included=np.zeros(M)\n",
239 |     "    for i in range(M):\n",
240 |     "        x=sampling(n)\n",
241 |     "        xmean=np.mean(x)\n",
242 |     "        xstd=np.std(x)\n",
243 |     "        lower=xmean-func.ndtri(1-alpha/2)*xstd/np.sqrt(n)\n",
244 |     "        upper=xmean+func.ndtri(1-alpha/2)*xstd/np.sqrt(n)\n",
245 |     "        # 如果包含真值\n",
246 |     "        #print(mu, lower, upper, mu>=lower, mu<=upper)\n",
247 |     "        if 0>=lower and 0<=upper:\n",
248 |     "            included[i]=1\n",
249 |     "    print(\"Sample size=%s, the prob. of included=\" % n, np.mean(included))"
250 |    ]
251 |   },
252 |   {
253 |    "cell_type": "code",
254 |    "execution_count": null,
255 |    "metadata": {
256 |     "collapsed": true
257 |    },
258 |    "outputs": [],
259 |    "source": []
260 |   }
261 |  ],
262 |  "metadata": {
263 |   "kernelspec": {
264 |    "display_name": "Anaconda",
265 |    "language": "python",
266 |    "name": "anaconda"
267 |   },
268 |   "language_info": {
269 |    "codemirror_mode": {
270 |     "name": "ipython",
271 |     "version": 3
272 |    },
273 |    "file_extension": ".py",
274 |    "mimetype": "text/x-python",
275 |    "name": "python",
276 |    "nbconvert_exporter": "python",
277 |    "pygments_lexer": "ipython3",
278 |    "version": "3.9.12"
279 |   },
280 |   "latex_envs": {
281 |    "LaTeX_envs_menu_present": true,
282 |    "autocomplete": true,
283 |    "bibliofile": "biblio.bib",
284 |    "cite_by": "apalike",
285 |    "current_citInitial": 1,
286 |    "eqLabelWithNumbers": true,
287 |    "eqNumInitial": 1,
288 |    "hotkeys": {
289 |     "equation": "Ctrl-E",
290 |     "itemize": "Ctrl-I"
291 |    },
292 |    "labels_anchors": false,
293 |    "latex_user_defs": false,
294 |    "report_style_numbering": false,
295 |    "user_envs_cfg": false
296 |   }
297 |  },
298 |  "nbformat": 4,
299 |  "nbformat_minor": 2
300 | }
301 | 


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/notebook_python/rejection_beta.pdf:
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