Products, and ratios for a bivariate gamma distribution

摘要

We derive the distributions of P = XY and W = X/(X + Y) and the corresponding moment properties when X and Y follow a bivariate gamma distribution. The expressions turn out to involve several special functions. We also provide extensive tabulations of the percentage points associated with the two distributions. These tables—obtained using intensive computing power—will be of use to practitioners of the bivariate gamma distribution.