JSM 2004 - Toronto

Abstract #301158

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Activity Number: 443
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Education
Abstract - #301158
Title: Finite Population Probability-generating Functions
Author(s): George R. Terrell*+ and Steven J. Kathman
Companies: Virginia Polytechnic Institute and State University and GlaxoSmithKline GlaxoSmithKline
Address: Statistics Dept., Blacksburg, VA, 24061,
Keywords: discrete distributions ; hypergeometric variables ; occupancy problems
Abstract:

Probability-generating functions (PGF) are an elegant device for deriving probability densities and moments for non-negative integer-valued random variables. Unfortunately, they cannot be expressed in elementary form for a number of important families, such as the hypergeometric. We propose an alternative form of generating function, the Finite Population Probability-generating Function (FPPGF), that takes an elementary form in many cases where the PGF does not. Interestingly, the FPPGF is as simple as the PGF for some important families, such as the binomial. It facilitates derivation of probability densities and moments in a similar way. We demonstrate its application to cases that were formerly considered difficult.

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