Multivariate Life Distributions Induced by Gamma Process Environments,

We develop a class of multivariate life distributions based on the notion that an unknown common environment induces dependencies. The environment is assumed to be dynamic and is described by a gamma process. The multivariate exponential distribution of Marshall and Olkin, motivated via an environment comprising of nonfatal Poisson shock processes wherein the probability of failure associated with each shock is the same, turns out to be a special case of our development. The gamma process environment reduces to a consideration of a Poisson shock model with the shocks having different probabilities of failure. AN