Journal of Applied Mathematics and Stochastic Analysis
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.
© 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.
Chukova, Stefanka; Dimitrov, Boyan N.; and Dion, Jean Pierre, "On Revelation Transforms that Characterize Probability Distributions" (1993). Mathematics Publications. 54.