Re: Log-normal distribution

From: andre (andrevh_at_sci.kun.nl)
Date: 10/26/04 

Date: Tue, 26 Oct 2004 16:40:58 +0000 (UTC)

vhchea@walla.com (Ernest Chea) wrote:
>Hie,
>
>I've been thinking of these problems for quite sometime now. I've been
>given a value of mean and its standard deviation while the
>distribution given is a log-normal distribution. I aware that these
>given mean and sd cannot be used directly. We need to actually change
>the value to natural log based in order to apply it appropriately.
>After searching through the web and my statistic book, I can't found
>anyway near to really give me a hints how to do it.
>Anyone out there, can you please help out.
>If you found that my explaination is not good enough, pls let me know.
>
>Thanks a lot!
>
>Best Rgds
>VH Chea

First on the list after Google "log normal distribution" leads to
"http://mathworld.wolfram.com/LogNormalDistribution.html" where I find

  mu = exp(M+S^2/2)
  si^2 = exp(M/2+S^2)*(exp(S^2)-1)

Some algebra gives

  M = ln(mu) - S^2/2
  S^2 = ln(si^2/mu) - ln(1-exp(-S^2))

The last equation can be solved numerically for S^2, or (I guess) recursively
following

 S(n)^2 = ln( si^2/mu ) - ln( 1-exp(-S(n-1)^2) )

with S(infinity)^2 as solution. Am I right that S(0)^2 = ln(si^2/mu) is the
approximation you are talking about?