Help with Program that Demonstrates Central Limit Theorem Nested Loop

[Jason Browen]

Dear all,

I am using Stata 16, on mac. The following program I included selects a particular number of observations from a Chi-Square distribution.

cap program drop randdraw

program define randdraw

clear

args N distribution

set obs `N'

gen x = `distribution'

sum

end

simulate mean_x =r(mean), reps(1000): randdraw 50 "rchi2(2)"


If I I wanted to write a nested loop that will simulate drawing a sample mean from a uniform distribution, poisson distribution, and beta distribution from with sample sizes of 3, 40, 500, and 1,000, replicate each 500 times and plot a histogram of the resulting distribution of the sample means. So that the first histogram will have 500 observations of sample means taken from 3 observations drawn according to the underlying distribution, the second will have 500 observations of sample means taken from 50 observations, etc. Am I able to use the program that I listed previously?


Thank you in advance for your help


Jason Browen

[Clyde Schechter]

Well, the code you show will generate 1000 means of 50 draws from a chi2 distribution with 2df. It won't plot a histogram, and it won't do any other sample sizes. So it seems you want to embellish the code a bit and then wrap it in a loop over sample size.

clear*

cap program drop randdraw
program define randdraw
    clear
    args N distribution
    set obs `N'
    gen x = `distribution'
    summ
end

set seed 1234

foreach ss of numlist 3 40 500 1000 {
    simulate mean_x =r(mean), reps(1000) : randdraw `ss' "rchi2(2)"
    histogram mean_x, name(sample_size_`ss', replace)
}

[Jason Browen]

Thank for Clyde for your help!