Re: Suggestion Wanted: CI of Poisson times Gamma RV
From: Glen (glenbarnett_at_geocities.com)
Date: 08/30/04
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Date: 29 Aug 2004 22:40:54 -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.
This is a little confusing. You might mean any of several things.
If the gamma-distributed "rate" you mention is the rate at which
defects occur, you don't want the product of the two random variables.
You're simply using the Poisson-Gamma distribution to model the process.
If "rate" means something else than the defect-rate (e.g. the cost of
each defect), then (assuming independence) you have a sum of gamma
random variables, but with the number of terms in the sum having a
Poisson distribution (a so-called compound Poisson). In this case
you /still/ don't want the product of the two random variables, though
the mean of the compound sum would be the product of the means.
Could you give more information about what you're trying to do?
Glen
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