Covariance identities for exponential and related distributions

[Bobkov and Houdre (1997] proved that if [xi], [eta] and [zeta] are independent standard exponential random variables, then for any two absolutely continuous functions f and g such that Ef([xi])2<[infinity] and Eg([xi])2<[infinity], the equality Cov(f([xi]),g([xi]))=Ef'([xi]+[eta])g'([xi]+[zeta]) holds. We prove that the identity holds if and only if [xi], [eta] and [zeta] or -[xi],-[eta] and -[zeta] are standard exponential random variables.

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Year of publication:	1999
Authors:	Rao, B. L. S. Prakasa
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 42.1999, 3, p. 305-311
Publisher:	Elsevier
Subject:	Exponential distribution Characterization Covariance identity

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005254567