On a Bivariate Distribution with Exponential Marginals

Abstract

A new bivariate distribution with exponential marginals has been introduced by Singpurwalla & Youngren (1993). This distribution is absolutely continuous and has a single parameter. It was originally motivated as the failure model for a two‐component system experiencing damage described by a shot–noise process. The purpose of this paper is two‐fold. The first is to articulate on several aspects of this distribution, in particular, its genesis, the nature of its dependence, its correlation structure, and its generalized version as a two‐parameter bivariate distribution with exponential marginals. The second purpose of this paper is more general. Prompted by the need to explain certain features of the bivariate distribution, it is found useful to introduce a new notion in reliability and survival analysis. This notion is called the “hazard potential”, of an item susceptible to failure. The hazard potential is viewed as a kind of hidden parameter of failure models that delineates a cause and effect relationship in reliability.