Abstract: The constancy of the conditional expectation of some suitable functions of record values no some others, is used to characterize the exponential or geometric distribution among the class of continuous or discrete distributions, respectively. Some characterizations of the homogeneous Poisson process in the class of nonhomogeneous Poisson processes through properties of arrival times, current life and residual life are also given.
Key words and phrases: Characterization, exponential distribution, geometric distribution, Poisson process, record values.