Re: Approximate a Lognormal by sum of Gaussian

Herman Rubin wrote:
In article
<32124213.1169507947458.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Jack Tomsky <jtomsky@xxxxxxxxxxxxx> wrote:
My friend told me that I can approximate a lognormal
distribution
(acutally any function) by a sum of several Gaussian
functions. I tried
to google the detail, but returned so many unrelated
links. I want to
know how to find out the parameters for the Gaussian
functions and the
error term. If you happen to know good references or
some keywords,
please leave a message. Thank you.




The sum of several Gaussians is itself a Gaussian. Therefore, you
need only a single Gaussian. What your friend probably meant was
that the log of a lognormal is a Gaussian. That Gaussian could
then
be decomposed into several Gaussians if that is of interest.

The question is not approximating a lognormal random variable
by a sum of normal random variable, but a lognormal distribution
by a sum (rather, linear combination) of normal distributions.

AFAIK, there is no good way of doing this.

... to say anything more specific, the OP would need to say whether
the use of negative coefficients in the sum of distribution functions
would be acceptable.

David Jones


.

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