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AGING FUNCTIONS AND MULTIVARIATE NOTIONS OF NBU AND IFR

Published online by Cambridge University Press:  18 March 2010

Fabrizio Durante ,
Rachele Foschi  and
Fabio Spizzichino
Fabrizio Durante
Affiliation:
Department of Knowledge-Based Mathematical Systems, Johannes Kepler UniversityA-4040 Linz, Austria E-mail: fabrizio.durante@jku.at
Rachele Foschi
Affiliation:
Dipartimento di Matematica, University “La Sapienza”I-00185 Rome, Italy E-mail: foschi@mat.uniroma1.it, fabio.spizzichino@uniroma1.it
Fabio Spizzichino
Affiliation:
Dipartimento di Matematica, University “La Sapienza”I-00185 Rome, Italy E-mail: foschi@mat.uniroma1.it, fabio.spizzichino@uniroma1.it
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Abstract

For d≥2, let X=(X1, …, Xd) be a vector of exchangeable continuous lifetimes with joint survival function . For such models, we study some properties of multivariate aging of that are described by means of the multivariate aging function , which is a useful tool for describing the level curves of . Specifically, the attention is devoted to notions that generalize the univariate concepts of New Better than Used and Increasing Failure Rate. These multivariate notions are satisfied by random vectors whose components are conditionally independent and identically distributed having univariate conditional survival function that is New Better than Used (respectively, Increasing Failure Rate). Furthermore, they also have an interpretation in terms of comparisons among conditional survival functions of residual lifetimes, given a same history of observed survivals.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 2 , April 2010 , pp. 263 - 278
Copyright
Copyright © Cambridge University Press 2010

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