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Subject: Re: Approximation sum of 2 lognormal RVs
Date: Tue, 30 Dec 2008 00:34:02 +0000 (UTC)
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"Pete sherer" <tsh@abg.com> wrote in message <gjbn6e$d62$1@fred.mathworks.com>...
> I am looking for a function that can approximate parameters (mean and sigma) for the sum of 2 lognormal distributions. I know the mean and sigma of log(X) and log(Y).  The question is how to estimate the mean and sigma of (Z) and its distribution if not lognormal (assuming Z = X + Y).

  Are you assuming X and Y are independent random variables?  If so, the Wikipedia website at

 http://en.wikipedia.org/wiki/Log-normal_distribution

has all the information you need to answer your question.  Just add the two expressions for the means, E(X) and E(Y), given there.  The standard deviation comes from

 sigma^2 = E((Z-E(Z))^2) = 
 E((X-E(X))^2 + E((Y-E(Y))^2) = var(X) + var(Y)

and these are also given in the website.

  (I assume that by your remark "and its distribution if not lognormal" you meant that Z would not be lognormal.)

Roger Stafford