ABSTRACT
Various generalizations of the univariate exponential distribution to model life times of the components of a multivariate system have been proposed. The usefulness of any such model depends on its probabilistic enhancement and its amenability to statistical inference. Tests for parameters of the underlying distribution are of prime interest. Reliability theory abounds with many multivariate distributions. This chapter considers some of them, giving compact representations of their densities and develops optimal tests for their parameters. These include the Marshall-Olkin, Block-Basu, Freund, Arnold- Strauss, Gumbel I, II, and III, models, etc. The chapter discusses non-regular models and reviews well known results as well as very recent ones. The trivial generalization to a multivariate exponential model from a univariate one may be that of independent exponential components. Even in this simplest model, however, optimality of tests in simultaneous inference can be quite interesting.
