Discrete Approximations to Continuous Univariate Distributions—an Alternative to Simulation

Summary 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 corresonding 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.