Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 4, Pages 345-357
On revelation transforms that characterize probability
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 S. Chukova et al. 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.
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. , and Lau
and Rao  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.