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Characterizations via conditional distributions

Published online by Cambridge University Press:  14 July 2016

Robert H. Berk
Robert H. Berk*
Affiliation:
Rutgers University
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Abstract

For independent random variables X and Y, if the conditional distribution of X given X + Y satisfies certain conditions, then the joint distribution of X and Y is a member of a certain one-parameter exponential family. Extensions for n independent random variables are given. A characterization for independent random variables involving order statistics is also given.

Keywords

CHARACTERIZATIONCONDITIONAL DISTRIBUTIONEXPONENTIAL FAMILY
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 4 , December 1977 , pp. 806 - 816
Copyright
Copyright © Applied Probability Trust 1977 

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Footnotes

Research supported by Grant MCS 75–23344 from the U.S. National Science Foundation.

References

De Bruijn, N. G. (1966) On almost additive functions. Colloq. Math. 15, 59–63.Google Scholar
Doróczy, Z. and Losonczi, L. (1967) Über die Erweiterung der auf einer Punktmenge additiven Functionen. Publ. Math. Debrecen 14, 239–245.Google Scholar
Galambos, J. (1975) Characterizations of probability distributions by properties of order statistics I. In Statistical Distributions in Scientific Work Vol. III, ed. Patil, G. P. et al. Reidel, Dordrecht and Boston, 71–88.Google Scholar
Hipp, C. (1974) Sufficient statistics and exponential families. Ann. Statist. 2, 1283–1292.Google Scholar
Jurkat, W. B. (1965) On Cauchy's functional equation. Proc. Amer. Math. Soc. 16, 683–686.Google Scholar
Kabe, D. G. (1969) On characterizing the multivariate linear exponential distribution. Canad. Math. Bull. 12, 567–572.Google Scholar
Mathai, A. M. (1967) On the structural properties of the conditional distributions. Canad. Math. Bull. 10, 239–245.Google Scholar
Menon, M. V. (1966) Characterization theorems for some univariate probability distributions. J. R. Statist. Soc. B 28, 143–145.Google Scholar
Patil, G. P. and Seshadri, V. (1964) Characterization theorems for some univariate probability distributions. J. R. Statist. Soc. B 26, 286–292.Google Scholar
Sen, P. K. (1970) A note on order statistics for heterogeneous distributions. Ann. Math. Statist. 41, 2137–2139.Google Scholar