Memory as a Property of Probability Distributions

The probability law of a positive random variable with finite mean is uniquely determined by the mean residual life (MRL) function. This function is useful as an indicator of aging and similar mechanisms. Memory is defined and several measures of memory are derived from the MRL function. Properties of the MRL function and the hazard function are compared. A class of distributions with convex decreasing MRL function, which forms a proper subset of the class of distributions with increasing hazard function, is defined. It is indicated how representative distributional models can be constructed from data.