On revelation transforms that characterize probability distributions

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.