Aging functions and multivariate notions of nbu and ifr

  • Authors:

  • Fabrizio Durante;Rachele Foschi;Fabio Spizzichino

  • Affiliations:

  • Department of knowledge-based mathematical systems, johannes kepler universitya-4040 linz, austria e-mail: fabrizio.durante@jku.at;Dipartimento di matematica, university “la sapienza”i-00185 rome, italy e-mail: foschi@mat.uniroma1.it, fabio.spizzichino@uniroma1.it;Dipartimento di matematica, university “la sapienza”i-00185 rome, italy e-mail: foschi@mat.uniroma1.it, fabio.spizzichino@uniroma1.it

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2010

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Abstract

For d≥2, let X=(X1, …, Xd) be a vector of exchangeable continuous lifetimes with joint survival function $\overline{F}$. For such models, we study some properties of multivariate aging of $\overline{F}$ that are described by means of the multivariate aging function $B_{\overline{F}}$, which is a useful tool for describing the level curves of $\overline{F}$. 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.