It is the scale factor that causes the probability distribution of X to not be Pois(lambda). The calculation is trivial. But I believe the original poster was searching for a name, and "Poisson", in the strictest sense, is not it.
On Tue, May 12, 2009 at 9:38 AM, Robert A LaBudde <ral@lcfltd.com> wrote:
Suppose X = A*N, where A is a scalar constant and N ~ Pois(lambda).
Then P[X = x] = P[N = x/A] ~ Pois(lambda).
I.e., X has the same probability mass distribution as N, except for a scale factor of A on the assumed values.
I think you are thinking this problem is complex, when, in fact, it is trivial.
At 07:41 AM 5/12/2009, Jewel Bright wrote:
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
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS e-mail: ral@lcfltd.com
Least Cost Formulations, Ltd. URL: http://lcfltd.com/
824 Timberlake Drive Tel: 757-467-0954
Virginia Beach, VA 23464-3239 Fax: 757-467-2947
"Vere scire est per causas scire"
================================================================
--------------------------------------------------------------------
This message was distributed by s-news@lists.biostat.wustl.edu. To
unsubscribe send e-mail to s-news-request@lists.biostat.wustl.edu with
the BODY of the message: unsubscribe s-news
|