Diagonal sections of copulas, multivariate conditional hazard rates and distributions of order statistics for minimally stable lifetimes

Abstract

As a motivating problem, we aim to study some special aspects of the marginal distributions of the order statistics for exchangeable and (more generally) for minimally stable non-negative random variables T1, ..., Tr. In any case, we assume that T1, ..., Tr are identically distributed, with a common survival function ̄G and their survival copula is denoted by K. The diagonal sections of K, along with ̄G, are possible tools to describe the information needed to recover the laws of order statistics.

Keywords

• minimally stable random vectors
• diagonal sections of survival copulas
• diagonal dependence
• t-exchangeability
• absolute continuity
• archimedean copulas
• load-sharing models
• 60e05
• 62h05
• 62g30
• 60k10
• 62n05