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Some Characterizations of the One-Parameter Family of Probability Distributions

Published online by Cambridge University Press:  20 November 2018

A. M. Mathai
A. M. Mathai*
Affiliation:
McGill University
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We consider one-parameter families of distributions which are of the general exponential type, the general series distribution type, or which can be transformed into the exponential type by a one-to-one transformation. In this paper we establish theorems to the effect that such distributions may be characterized by a simple differential equation involving the mean function. It is illustrated that almost all the classical one-parameter families of distributions are characterized by these theorems. Multivariate generalizations are given, and it is also noticed that the functional form of the normalizing factor determines the specific distribution in each general family.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 1 , April 1966 , pp. 95 - 102
Copyright
Copyright © Canadian Mathematical Society 1966

References

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