A Characterization of a Bivariate Exponential Distribution

Abstract

The independence of $U = \min (X, Y)$ and $V = X - Y$ or $W = |X - Y|$ is studied where $X$ and $Y$ are not assumed to be independent. The bivariate exponential distribution of Marshall and Olkin is characterized as the distribution with exponential marginals where $U$ is exponential and independent of $V$.