Sums, products, and ratios for the bivariate gumbel distribution

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