23 Multivariate exponential distributions and their applications in reliability

Abstract

Publisher Summary This chapter discusses the multivariate exponential distributions and their applications in reliability. The univariate exponential distribution is well known as a model in reliability theory. Because of the usefulness of the univariate exponential distribution it is natural to consider multivariate exponential distributions as models for multicomponent systems. However, there is no natural extension available in a unique way. The chapter presents a survey of bivariate exponential distributions, the important multivariate extensions, and discusses the important multivariate extensions. Initial attempts have been to obtain a bivariate exponential distribution with exponential marginals without any appealing physical interpretations. The chapter also discusses Gumbel's distributions, Freund's model, Marshall–Olkin model, Block–Basu model, Friday and Patil distribution, Downton distribution, and other bivariate distributions.