Product of triangular distributions with range [0, 1]

Abstract

Where random variables have unknown distributions approximated by triangular distributions, products of random variables cannot be derived, so we are left to observe random samples of such a product and hope it might be well approximated with some familiar distribution. Parameters of the beta distribution are expressed as a second-degree polynomial in c1 and c2, where c1 and c2 are the modes of triangular distributions to be multiplied. Given observations of the responses α1 and α2, and corresponding independent variables c1 and c2, we model the beta distribution parameters as multiple linear functions of their original triangular distribution parameters c1 and c2. Evidence suggests that the product of independent triangular random variables has the approximate distribution of the beta with parameters that are functions of the original triangular random variables’ parameters.