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A characterization of the gamma distribution from a random difference equation

Published online by Cambridge University Press:  14 July 2016

Eric S. Tollar
Eric S. Tollar*
Affiliation:
The Florida State University
*
∗ Present address: Bell Communications Research, Rm 2Z-222, 331 Newman Springs Road, Red Bank, NJ 07701–7020, USA.
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Abstract

A characterization of the gamma distribution is considered which arises from a random difference equation. A proof without characteristic functions is given that if V and Y are independent random variables, then the independence of V · Y and (1 – V) · Y results in a characterization of the gamma distribution (after excluding the trivial cases).

Keywords

INDEPENDENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 142 - 149
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

Research supported in part by the U.S. Army Research Office Grant Number DAAG 29–82-K-0168.

The United States Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.

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