*** this prgram takes samples of varying sizes from known distributions to demonstrate the central limit theorem  ***


clear
** 1000 obs to have the repeated drawing of samples ***
set obs 1000

*** generate 50 columns of data, to be used in varying n's i.e. 1,2,5,10,20,50 to calculate means ***
*** this one is using the uniform distribution as the underlying distribution **
***
forvalues i=1/50 { 
gen unif`i'=runiform()
 }

 
*** note that the above code is the same as writing out the following ***
*** gen unif1=runiform()
*** gen unif2=runiform()
*** gen unif3=runiform()
*** gen unif4=runiform()
*** gen unif5=runiform()
*** gen unif6=runiform()
*** etc.
*** etc.
*** etc.
*** gen unif49=runiform()
*** gen unif50=runiform()
 
 
 ** repeated samples with n=1 in each sample**
 gen m1=unif1
histogram m1, percent fcolor(blue) normal normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 1, size(small)) name(hist_unif_1, replace)

** repeated samples with n=2 in each sample **
egen m2=rowmean(unif1-unif2)
histogram m2, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 2 from uniform dist , size(small)) name(hist_unif_2, replace)

** repeated samples with n=5 in each sample **
egen m5=rowmean(unif1-unif5)
histogram m5, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 5 from uniform dist, size(small)) name(hist_unif_5, replace)

** repeated samples with n=10 in each sample **
egen m10=rowmean(unif1-unif10)
histogram m10, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 10 from uniform dist, size(small)) name(hist_unif_10, replace)

** repeated samples with n=20 in each sample **
egen m20=rowmean(unif1-unif20)
histogram m20, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 20 from uniform dist, size(small)) name(hist_unif_20, replace)

** repeated samples with n=50 in each sample **
egen m50=rowmean(unif1-unif50)
histogram m50, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 50 from uniform dist, size(small)) name(hist_unif_50, replace)

graph combine hist_unif_1 hist_unif_2 hist_unif_5 hist_unif_10  hist_unif_20 hist_unif_50, name(unifgraphs, replace)








** now using the chi square distribution ***

clear
set obs 1000

forvalues i=1/50 { 
gen chisq`i'=rchi2(1)
 }
 
 
 summ chisq1, detail
 ** repeated samples with n=1 in each sample **
 hist chisq1, normal
 histogram chisq1, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 1 from Chi-square dist, size(small)) name(hist_ch1, replace)

** repeated samples with n=2 in each sample **
 egen ch2=rowmean(chisq1-chisq2)
  summ ch2, detail
 histogram ch2, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 2 from Chi-square dist, size(small)) name(hist_ch2, replace)

 ** repeated samples with n=5 in each sample**
 egen ch5=rowmean(chisq1-chisq5)
 histogram ch5, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 5 from Chi-square dist, size(small)) name(hist_ch5, replace)

 ** repeated samples with n=10 in each sample**
 egen ch10=rowmean(chisq1-chisq10)
 summ ch10, detail
 histogram ch10, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 10 from Chi-square dist, size(small)) name(hist_ch10, replace)

 ** repeated samples with n=20 in each sample**
 egen ch20=rowmean(chisq1-chisq20)
 histogram ch20, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 20 from Chi-square dist, size(small)) name(hist_ch20, replace)

 ** repeated samples with n=50 in each sample**
 egen ch50=rowmean(chisq1-chisq50)
 histogram ch50, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 50 from Chi-square dist, size(small)) name(hist_ch50, replace)


 graph combine hist_ch1 hist_ch2 hist_ch5 hist_ch10 hist_ch20 hist_ch50 , name(chihists,replace)
 


** now using the poisson distribution, with lambda=1.5 ***

clear
set obs 1000
 
 
forvalues i=1/50 { 
gen poiss`i'=rpoisson(1.5)
 }
 
 
 ** repeated samples with n=1 in each sample **
 histogram poiss1, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 1 from Poisson dist, size(small)) name(hist_pois1, replace)

** repeated samples with n=2 in each sample **
 egen p2=rowmean(poiss1-poiss2)
  summ p2, detail
 histogram p2, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 2 from Poisson dist, size(small)) name(hist_pois2, replace)

 ** repeated samples with n=5 in each sample**
 egen p5=rowmean(poiss1-poiss5)
 histogram p5, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 5 from Poisson dist, size(small)) name(hist_pois5, replace)

 ** repeated samples with n=10 in each sample**
 egen p10=rowmean(poiss1-poiss10)
 histogram p10, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 10 from Poisson dist, size(small)) name(hist_pois10, replace)

 ** repeated samples with n=20 in each sample**
 egen p20=rowmean(poiss1-poiss20)
 histogram p20, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 20 from Poisson dist, size(small)) name(hist_pois20, replace)

 ** repeated samples with n=50 in each sample**
 egen p50=rowmean(poiss1-poiss50)
 histogram p50, percent fcolor(blue) normal  normopts(lcolor(magenta) lwidth(medthick)) title(Means of samples of size 50 from Poisson dist, size(small)) name(hist_pois50, replace)


 graph combine hist_pois1 hist_pois2 hist_pois5 hist_pois10 hist_pois20 hist_pois50 , name(poishists,replace)