Discrete approximations to continuous univariate distributions - An alternative to simulation

Abstract

A method to replace a continuous univariate distribution with a discrete distribution that takes MN different values is analysed. Both distributions share the same rth moments for r = 0, . . ., 2N - 1 and their corresponding distribution functions coincide at least at M + 1 points. Several statistical and engineering examples are considered in which the discrete approximation may be used to avoid a simulation study that would be much more demanding computationally.