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st: RE: simulating a lognormal distribution


From   "Feiveson, Alan H. \(JSC-SK311\)" <alan.h.feiveson@nasa.gov>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: simulating a lognormal distribution
Date   Tue, 12 Sep 2006 08:56:59 -0500

Jeph - Let X = log(Y). You can use the fact that E(exp(tX)) = exp(mu*t +
t*t*sig2/2) where X~N(mu,sig2). Taking t=1,we see that E(Y) = mu +
sig2/2. Also the median of Y is exp(median of X) = exp(mu). So from the
mean and median of Y, you can get values for mu and sig. The sd of Y
adds additional information if you want to use it. Taking t=2, gives
E(Y^2) = E( (exp(x))^2 ) = E(exp(2X)) = 2*mu + 4*sig2/2 = 2*mu + 2*sig2.



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