Re: Fit to Poisson Distribution

From: Ross Clement (clemenr_at_wmin.ac.uk)
Date: 06/28/04 

Date: 28 Jun 2004 15:37:34 -0700

I'm no statistical expert, so I'm just "having a go" until a "proper
statistician" answers.

First, while your method gives an estimation of your underlying model
(poisson mean/var m plus a constant a). However, I can't see (may be
my fault) that taking the observed variance, and calculating the
constant a from it will give you the best estimate of the two
parameters. But, to know the "best" estimate of the parameters
requires a definition of "best".

One potential "best" would be the maximum likelihood estimation of the
two parameters. The usual example used to illustrate MLE is the
derivation of MLE for mean and sd of the normal distribution. E.g.

http://statgen.iop.kcl.ac.uk/bgim/mle/sslike_1.html

This page describes (most of the way down the page) MLE for standard
poisson.

http://mathworld.wolfram.com/MaximumLikelihood.html

Surely (unless I'm mistaken, which is quite probable :-) ) you could
use similar methods to develop MLE for m and a in your model.

Cheers,

Ross-c