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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

Information

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

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