Sums, products and ratios for Mckay’s bivariate gamma distribution

Motivated by hydrological applications, we derive the exact distributions of R=X+YR=X+Y, U=XY and W=X/(X+Y)W=X/(X+Y) and the corresponding moment properties when XX and YY follow McKay’s bivariate gamma distribution. The expressions turn out to involve several special functions. We also provide computer programs for generating tabulations of the percentage points associated with the distributions.