A CHARACTERIZATION OF THE EXPONENTIAL-DISTRIBUTION INVOLVING ABSOLUTE DIFFERENCES OF IID RANDOM-VARIABLES

Abstract

A probability measure mu on [0, infinity) is said to have property H if for independent random variables X1 and X2 distributed according to mu the absolute difference X1 - X2 has the same distribution. Continuing previous work of Puri and Rubin we characterize the set of all distributions having property H.