Sums, products, and ratios for Freund’s bivariate exponential distribution

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