Distribution combining program

摘要

The Distribution Combining Program is a set of algorithms that evaluates the probability distribution of the sum, difference, product, or ratio of two random variables with specified distributions. The method allows for correlation between the two input variables. The input distributions are assumed to be from the semi-normal family (i.e., with density function that is composed of two normalized halves of normal densities with generally different variances). The resultant distribution is approximated by a distribution of the same type in order to provide subsequent use as an input in a series of operations.

The program uses the technique of calculating several moments of the output distribution from the moments of the input distributions. This method avoids using Monte Carlo simulations, or any numerical evaluation of the convolution integrals. The program can be used in risk analysis, subjective probability evaluation, sensitivity analysis and similar situations. It is particularly suitable to replace Monte Carlo methods where correlated variables are involved, or when rapid execution is desired.