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Identically distributed linear forms and the normal distribution

Published online by Cambridge University Press:  01 July 2016

S. G. Ghurye  and
I. Olkin
S. G. Ghurye
Affiliation:
University of Alberta
I. Olkin
Affiliation:
Stanford University
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Abstract

A general discussion and survey is provided of the characterization of the normal distribution by the identical distribution of linear forms. The first result dates to 1923 when Pólya showed that if X and Y are i.i.d. random variables satisfying certain conditions, and if aX + bY is distributed as (a2 + b2)1/2X, then X has a normal distribution. This result has been generalized in several directions. In addition to a recasting of some of the results, an extension in the multivariate case is provided.

Keywords

CHARACTERIZATION OF PROBABILITY DISTRIBUTIONSIDENTICALLY DISTRIBUTED LINEAR FORMSNORMAL DISTRIBUTION, CHARACTERIZATION OFFUNCTIONAL EQUATIONS AND CHARACTERIZATIONS
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 1 , April 1973 , pp. 138 - 152
Copyright
Copyright © Applied Probability Trust 1973 

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References

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