Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-15T05:51:33.057Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Ferguson, T. S., Location and scale parameters in exponential families of distributions. Ann. MathStatist. 33 (1962a), pages 986-1001.Google Scholar
2. Ferguson, T. S., A characterization of the geometric distribution. Ann. Math. Statist. 33 (1962b), page 1207.Google Scholar
3. Laha, R. G., On the laws of Cauchy and Gauss. Ann. MathStatist. 30 (1955), pages 1165-1174.Google Scholar
4. Mathai, A. M., Some characterizations of the one parameter family of distributions. Canadian MathBull. 9 (1966), pages 95-102.Google Scholar
5. Mauldon, J. G., Characterization properties of statistical distributions. QuartJ.Math. 7 (1966), pages 155-160.Google Scholar
6. Moran, P. A. P., A characteristic property of the Poisson distribution. Proc. Cam. Phil. Soc. 48 (1955), pages 206-207.Google Scholar
7. Patil, G. P. and Seshadri, V., A characterization of a bivariate distribution by the marginal and the conditional distributions of the same component. Ann. Inst. Statist. MathTokyo, 15 (1966), pages 215-221.Google Scholar
8. Patil, G. P. and Seshadri, V., Characterization theorems for some univariate probability distributions. Roy. Statist. Soc. Series B. 26 (1966), pages 286-292.Google Scholar
9. Sierpinski, W., Sur 1'equation fonctionnelle f(+;y) = f(x) + f(y) Fund. Math. 1 (1922), pages 116-122.Google Scholar