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A characterization of the gamma distribution by the negative binomial distribution

Published online by Cambridge University Press:  14 July 2016

Jan Engel  and
Mynt Zijlstra
Jan Engel*
Affiliation:
N. V. Philips, Eindhoven
Mynt Zijlstra*
Affiliation:
N. V. Philips, Eindhoven
*
∗N. V. Philips, ISA-Quantitative Methods, Building HSM–301, 5600 MD Eindhoven, The Netherlands.
∗N. V. Philips, ISA-Quantitative Methods, Building HSM–301, 5600 MD Eindhoven, The Netherlands.
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Abstract

It is proved that for a Poisson process there exists a one-to-one relation between the distribution of the random variable N(Y) and the distribution of the non-negative random variable Y. This relation is used to characterize the gamma distribution by the negative binomial distribution. Furthermore it is applied to obtain some characterizations of the exponential distribution.

Keywords

GAMMA DISTRIBUTIONNEGATIVE BINOMIAL DISTRIBUTIONCHARACTERIZATIONPOISSON PROCESSGEOMETRIC DISTRIBUTIONEXPONENTIAL DISTRIBUTIONMOMENT PROBLEM
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 1138 - 1144
Copyright
Copyright © Applied Probability Trust 

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