Relations between ageing and dependence for exchangeable lifetimes with an extension for the IFRA/DFRA property

Nappo Giovanna () and Spizzichino Fabio ()
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Nappo Giovanna: Sapienza, Università di Roma,Italy
Spizzichino Fabio: Sapienza, Università di Roma,Italy

Dependence Modeling, 2020, vol. 8, issue 1, 1-33

Abstract: We first review an approach that had been developed in the past years to introduce concepts of “bivariate ageing” for exchangeable lifetimes and to analyze mutual relations among stochastic dependence, univariate ageing, and bivariate ageing.A specific feature of such an approach dwells on the concept of semi-copula and in the extension, from copulas to semi-copulas, of properties of stochastic dependence. In this perspective, we aim to discuss some intricate aspects of conceptual character and to provide the readers with pertinent remarks from a Bayesian Statistics standpoint. In particular we will discuss the role of extensions of dependence properties. “Archimedean” models have an important role in the present framework.In the second part of the paper, the definitions of Kendall distribution and of Kendall equivalence classes will be extended to semi-copulas and related properties will be analyzed. On such a basis, we will consider the notion of “Pseudo-Archimedean” models and extend to them the analysis of the relations between the ageing notions of IFRA/DFRA-type and the dependence concepts of PKD/NKD.

Keywords: bivariate ageing; semi-copulas; generalized Kendall distributions; positive Kendall dependence; pseudo-Archimedean semi-copulas; positive dependence orderings; Schur-costant models (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:8:y:2020:i:1:p:1-33:n:1

DOI: 10.1515/demo-2020-0001

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