Re: Related to Poisson

[courses@zanybooks.com]

A generalization of the central limit theorem (due I think to paul levy) says that all appropriately normalized sums of random variables converge to a normal plus the sum of generalized Poissons of the form you describe.  That is, if y(i) is 0 with probability 1 - lambda and takes the value A otherwise, then the sum of the Ay(i)'s will converge to the form that is of interest to you. (may have left an n off here).

 

 

 

-------- Original Message --------
Subject: [S] Related to Poisson
From: Jewel Bright <jwlbright@yahoo.com>
Date: Tue, May 12, 2009 4:41 am
To: s-news@lists.biostat.wustl.edu

Folks:

 

I have a seemingly simple question, but cannot resolve it (at least without much of thinking and digging.

 

Suppose that "n" is a Poisson random variable drawn from the distribution with Poisson lambda "lambda". What is the distribution of the random variable A*n, where A is an arbitrary real number?

 

Please, note, I am not asking how to generate this random variable, I still remember how to multiply a set of numbers by a constant. I am asking about analytical form of this distribution, and about how to derive the distribution function (or density) in their analytical form.

 

A standard approach through the characteristic functions did not bring immediate success. I am sure there there are a lot of smart people in the list who would consider this problem very simple. Please, help.

 

Thanks in advance.

 

Jewel