Exogenous shock models: analytical characterization and probabilistic construction

Abstract

A new characterization for survival functions of multivariate failure-times arising in exogenous shock models with non-negative, continuous, and unbounded shocks is presented. These survival-functions are the product of their ordered and individually transformed arguments. The involved transformations may depend on the specific order of the arguments and must fulfill a monotonicity condition. Conversely, every survival function of that very form can be constructed using an exogenous shock model with independent and non-homogeneous shocks.

Exact simulation of continuous max-id processes

“…Examples of families of max-id random vectors with natural geometric descriptions of their exponent measures are given by Marshall-Olkin distributions [14], random vectors with reciprocal Archimedean copula [7], max-stable distributions [16] and exogenuous shock models [19]. The rest of the paper is organized as follows.…”