A computer method to calculate the convolution of statistical distributions

Abstract

It is becoming increasingly important to determine probability distributions of combinations of random variables. Convolution is a technique by which the distribution of a sum of random variables can be determined. This paper presents some simplifications in order to reduce the numerical integrations and computer time. In addition, the method may be used with empirical nonanalytic distributions. While Monte Carlo methods are also appropriate for calculating the distribution, convolution can give at least as much accuracy as Monte Carlo methods with a reduction in computation. Two applications are presented: one approximates the distribution of percent sand in an area, and the other indicates a method of determining sample size when using the distribution of means to approximate normality.