MULTIVARIATE DISTRIBUTIONS INDUCED BY DYNAMIC ENVIRONMENTS

We develop families of multivariate life distributions for items which operate in environments that are dynamic, and whose effects on the li felengths are described by certain stochastic processes. We motivate a nd consider two such processes: a gamma process and a version of the s hot-noise process. A consideration of the former results in a new fami ly of multivariate life distributions, a special case of which is the multivariate exponential of Marshall & Olkin. We are therefore able to provide an alternate motivation for this well known distribution. The inherent singularities of this distribution are explained by the fact that a gamma process can be decomposed as the sum of a countable numb er of jumps of random heights at a countable number of random points; associated with each jump is a probability of the simultaneous failure of two or more items. A consideration of the shot-noise process resul ts in another family of multivariate distributions, a special case of which is a new one parameter bivariate distribution with exponential m arginals.