On the Linear Combination of Laplace and Logistic Random Variables

The distribution of linear combinations of random variables arises explicitly in many areas of engineering. This has increased the need to have available the widest possible range of statistical results on linear combinations of random variables. In this note, the exact distribution of the linear combination α X+β Y is derived when X and Y are Laplace and logistic random variables distributed independently of each other. Extensive tabulations of the associated percentage points obtained by inverting the derived distribution are also given.