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On characterization of certain probability distributions

Published online by Cambridge University Press:  24 October 2008

Y. H. Wang
Y. H. Wang
Affiliation:
Division of Statistics, Ohio State University
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Introduction: Let X1, X2, …, Xn be n (n ≤ 2) independent observations on a random variable X with distribution function F. Also let L = L (X1, X2, …, Xn) be a linear statistic and Q = Q (X1, X2, …, Xn) be a homogeneous quadratic statistic. In this paper, we consider the problem of characterizing a class of probability distributions by the linear regression of the statistic Q on the other statistic L. In section 2, we obtain a characterization of a class of probability distributions, which includes the normal and the Poisson distributions. In section 3, a class of distributions including the gamma, the binomial and the negative binomial distributions is characterized.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 2 , March 1972 , pp. 347 - 352
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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