Some properties of ageing notions based on the moment-generating-function order

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Abstract

Classes of life distributions based on the moment-generating-function order are investigated in this paper. It is shown firstly that the class M is closed under both convex linear combination and geometric compounding. Secondly, the class NBU mg (new better than used in the moment-generating-function order) is proved to be closed under increasing star-shaped transformations. Finally, the interplay between the stochastic comparison of the excess lifetime of a renewal process and the NBU mg interarrivals is studied.

Original languageEnglish
Pages (from-to)927-934
Number of pages8
JournalJournal of Applied Probability
Volume41
Issue number3
DOIs
StatePublished - Sep 2004

Keywords

  • Convex linear combination
  • Convolution
  • Geometric compounding
  • M -class
  • M-class
  • NBU
  • Star-shaped transform

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