The distribution of sums, products and ratios for Lawrance and Lewis's bivariate exponential random variables

We derive the exact distributions of R=X+YR=X+Y, P=XYP=XY and W=X/(X+Y)W=X/(X+Y) and the corresponding moment properties when XX and YY follow Lawrence and Lewis'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.