Shock processes by aftereffects and multivariate lack of memory

Abstract

If the survival function satisfies the functional equation where e = (1, …, 1), and if the marginal distributions are exponential, then is the multivariate exponential distribution of Marshall and Olkin. The functional equation has many solutions if the requirement of exponential marginals is not imposed, but the class of possible marginals is somewhat limited (e.g., marginals must be absolutely continuous). The class of possible solutions of the equation is characterized in this paper, and several examples are obtained from models for dependence that may be of practical interest.