Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 4, Pages 345-357
doi:10.1155/S1048953393000292

On revelation transforms that characterize probability distributions

S. Chukova,1 B. Dimitrov,1 and J.-P. Dion2

1GMI Engineering and Management Institute, Department of Science and Mathematics, 1700 West Third Ave., Flint, MI 48504-4898, USA
2Universite du Quebec a Montreal, Case postale 8888, succursale “A”, (QC), Montreal H3C 3P8, Canada

Received 1 October 1993; Revised 1 November 1993

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A characterization of exponential, geometric and of distributions with almost-lack-of-memory property, based on the “revelation transform of probability distributions” and “relevation of random variables” is discussed. Known characterizations of the exponential distribution on the base of relevation transforms given by Grosswald et al. [4], and Lau and Rao [7] are obtained under weakened conditions and the proofs are simplified. A characterization the class of almost-lack-of-memory distributions through the relevation is specified.