Archimedean-based Marshall-Olkin Distributions and Related Copula Functions

TL;DR

This paper introduces a new class of bivariate distributions based on Archimedean and Marshall-Olkin frameworks, analyzing their dependence structures via copula functions, including asymmetry and tail dependence.

Contribution

It extends existing Marshall-Olkin distributions by incorporating Archimedean-based copulas, providing a broader class with asymmetric dependence features.

Findings

Includes special cases like Generalized Marshall-Olkin copulas

Studies asymmetry and tail dependence parameters

Analyzes Kendall's tau for the new copulas

Abstract

A new class of bivariate distributions is introduced that extends the Generalized Marshall-Olkin distributions of Li and Pellerey (2011). Their dependence structure is studied through the analysis of the copula functions that they induce. These copulas, that include as special cases the Generalized Marshall-Olkin copulas and the Scale Mixture of Marshall-Olkin copulas (see Li, 2009),are obtained through suitable distortions of bivariate Archimedean copulas: this induces asymmetry, and the corresponding Kendall's tau as well as the tail dependence parameters are studied.