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On the Structural Properties of the Conditional Distributions

Published online by Cambridge University Press:  20 November 2018

A.M. Mathai
A.M. Mathai*
Affiliation:
McGill University
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If x, x1,…, xn are independent stochastic variables and if the conditional distribution of x given x1 +…+ xn is known, what can be said about the marginal distributions of x, x1,…, xn? In this paper we will show that if the conditional distribution of x given a subset of x1, x2,…, xn-1, x+ x1 +…+ xn has a certain structural form then x, x1,…, xn are distributed as members of the linear exponential family of distributions and further x1,…, xn are identically distributed.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 2 , June 1967 , pp. 239 - 245
Copyright
Copyright © Canadian Mathematical Society 1967

References

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