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# st: RE: Central LImit Theory

 From "Nick Cox" To Subject st: RE: Central LImit Theory Date Wed, 11 Dec 2002 17:58:53 -0000

```Jitian Sheu

> Does anyone know how to demonstrate Central Limit Theory in Stata?

Here is one way to do it:

clear
set obs 10000
gen y = -10 * ln(uniform())
egen sample = seq(), b(100)
egen n = seq(), t(100)
forval i = 1/10 {
local n = `i'^2
qui egen mean = mean(y) if n <= `n', by(sample)
qnorm mean if n == 1, t1(sample size is `n') saving(qnorm`i')
more
dotplot mean if n == 1, t1(sample size is `n') saving(dotplot`i')
more
drop mean
}

You can clearly vary

1. # of samples (here always 100)
2. # in sample (here squares of 1(1)10)
3. distribution you sample from (here exponential with mean 10)
4. sampling design

Nick
n.j.cox@durham.ac.uk

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```

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