Marshall-Olkin copulas revisited

Abstract

Almost seventy years old Marshall-Olkin copulas, then wider Marshall copulas, and finally even wider shock model (SM) copulas constitute a substantial part of nowadays copula theory due to numerous applications. Recently, Christian Genest with some coauthors introduced a new stochastic model for a special subclass of SM copulas which gives not only a new angle on these copulas but also widens the range of applications. In this paper we extend this type of stochastic model to all known subclasses of SM copulas. We also introduce a novel class of SM copulas and extend the new stochastic model to this class as well.