Re: Suggestion Wanted: CI of Poisson times Gamma RV

From: Ray Koopman (koopman_at_sfu.ca)
Date: 08/27/04 

Date: 27 Aug 2004 03:03:26 -0700

Paige Miller <paige.miller@kodak.com> wrote in message
news:<cgi0dt$avb$1@news.kodak.com>...
> I have a Poisson random variable, representing the number of defects
> on a certain manufactured item. My estimator is this Poisson RV,
> times a rate value (rate > 0 and rate < infinity), which is itself a
> random variable, and which I for now I assume is distributed as a
> Gamma random variable.
>
> I want to find confidence intervals (or the distribution) for this
> particular estimator. I am stuck at this point, I don't know what to
> do next, I don't know how to proceed.

Am I reading this right? You have iid observations of a (continuous)
variable Z which you model as the product of a (discrete) Poisson
variable X times a (continuous) Gamma variable Y. You want a CI for
the mean of the X distribution. Is that all the information you have?

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