Marshall-Olkin copulas revisited

TL;DR

This paper revisits Marshall-Olkin copulas, extending a recent stochastic model to all subclasses of shock model copulas and introducing a new class, broadening theoretical understanding and potential applications.

Contribution

It generalizes a recent stochastic model to all subclasses of shock model copulas and introduces a novel class, expanding the scope of copula theory.

Findings

Extended stochastic model to all subclasses of SM copulas.

Introduced a new class of shock model copulas.

Broadened the applicability of copula models in theory and practice.

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.