Re: random numbers from a lognormal distribution
From: Reef Fish (Large_Nassau_Grouper_at_Yahoo.com)
Date: 02/13/05
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Date: 13 Feb 2005 10:35:21 -0800
Dave wrote:
> On Tue, 01 Feb 2005 20:33:15 -0600, Ray Koopman wrote:
> >Bob Wheeler wrote:
> >> [...]
> >> I think he is asking how to do it himself. If X is a standard
> normal variate, then U=(log(X)-m)/s is lognormal with mean
> exp(m)sqrt(w), where w=exp(s^2), and variance exp(2m)w(w-1).
> >
> >Shouldn't that be "If X is a standard normal variate then
> U=exp(X*s+m) is lognormal ..."?
< snip >
The confusion arises only if you trip yourself by other statistics
associated with the distribution(s).
How can there be any confusion if you simply recall that, X, by
definition, has a lognormal distribution if log X is normally
distributed?
Thus, if Y has ANY normal distribution, the exp(Y) is lognormal!
> So now whenever I work with the lognormal distribution, I use the
> median and interquartile range as my 2 pieces of information instead
> of the mean and standard deviation. Try it. I like it much better.
This addresses a different question, i.e., how do you generate
a lognormal distribution with some specification about either
the parent (normal) distribution or its resulting (lognormal)
distribution. But the simple, GENERAL priniciple, is that
exp(X) is lognormal whenever X is normal.
-- Bob.
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