Exact distributions of XY for some bivariate exponential distributions

摘要

The distribution of products of random variables is of interest in many areas of the sciences, engineering and medicine. This has increased the need to have available the widest possible range of statistical results on products of random variables. In this article, the exact distributions of P = XY and the corresponding moment properties are derived when X and Y follow six flexible bivariate exponential distributions. The expressions turn out to involve several special functions.