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Characterization theorems using conditional expectations

Published online by Cambridge University Press:  14 July 2016

Ignacy I. Kotlarski  and
William E. Hinds
Ignacy I. Kotlarski
Affiliation:
Oklahoma State University
William E. Hinds
Affiliation:
Denison University
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Abstract

Recent characterizations of probability measures by use of conditional expectations have included many probability measures defined on subsets of the real line. This paper contains results which allow similar characterizations by use of conditional expectations but are valid for probability measures defined on subsets of an arbitrary space. In the special case of a measure defined on subsets of R' the result is not always as sharp as known results, but these theorems can be applied to measures defined on subsets of Rn with n ≧ 1.

Keywords

CONDITIONAL EXPECTATIONCHARACTERIZATIONARBITRARY MEASURABLE SPACEEXPONENTIAL DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 400 - 406
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Hamdan, M. A. (1972) On a characterization by conditional expectation. Technometrics 14, No. 2, 497–499.CrossRefGoogle Scholar
[2] Kotlarski, I. I. (1973) On a characterization of some probability distributions by conditional expectations. Sankhya , A 34, 461–467.Google Scholar
[3] Shanbhag, D. N. (1970) The characterizations for exponential and geometric distribution. J. Amer. Statist. Assoc. 65, 1256–1259.Google Scholar