# st: RE: iid draw from a truncated normal distribution

 From "Steichen, Thomas J." To "'statalist@hsphsun2.harvard.edu'" Subject st: RE: iid draw from a truncated normal distribution Date Mon, 22 Sep 2008 09:30:09 -0400

```P(z>2 | mean=0, sd=1) = .000031 (about 3 in 100,000).

Thus it is quite unlikely that the extremes in a sample of 10,000 will approach or exceed +/- 2. So, your truncation points are not shifted; rather, they are so extreme as to be seldom reached (thus the _apparent_ truncation points will be well within +/- 2).

-----------------------------------
Thomas J. Steichen
steicht@rjrt.com
-----------------------------------

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Alexander Kalb
Sent: Monday, September 22, 2008 9:18 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: iid draw from a truncated normal distribution

I would like to create an iid draw form a truncated normal distribution
(on the left and right side) with standard deviation 0.5 (in the
untruncated case). I tried the following commands:

set obs 10000
gen c = -2  /*left truncation point*/
gen d = 2 /*right truncation point*/
gen stdv = 0.5  /*standard deviation*/
gen v = uniform()
gen c_bar = c/stdv
gen d_bar = d/stdv
gen v_bar = (normal(c_bar) + (normal(d_bar) - normal(c_bar))*v)
gen u = stdv*invnorm(v_bar)

This seems to work but it shifts the truncation points below 2 and
above -2. Has anybody an idea how I can get an iid draw (with standard
deviaton of 0.5 in the untruncated case) which does not shift the
truncation points?

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