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.