One-factor lévy-frailty copulas with inhomogeneous trigger rates

Abstract

Anewparametric family of high-dimensional, non-exchangeable extremevalue copulas is presented. The construction is based on the Lévy-frailty construction and stems from a subfamily of the Marshall–Olkin distribution. In contrast to the classical Lévy-frailty construction, non-exchangeability is achieved by inhomogeneous trigger-rate parameters. This family is studied with respect to its distributional properties and a sampling algorithm is developed. Moreover, a new estimator for its parameters is given. The estimation strategy consists in minimizing themean squared error of the underlying Bernstein function and certain strongly consistent estimates thereof.