The extreme points of the set of decreasing failure rate distributions

Naftali A. Langberg, Ramón V. León, James Lynch, Frank Proschan

Research output: Contribution to journalArticlepeer-review

Abstract

Since the class of extended decreasing failure rate (EDFR) life distributions (i.e., distributions with support in [0, ∞]) is compact and convex, it follows from Choquet's Theorem that every EDFR life distribution can be represented as a mixture of extreme points of the EDFR class. We identify the extreme points of this class and of the standard class of decresing failure rate (DFR) life distributions. Further, we show that even though the convex class of DFR life distributions is not compact, every DFR life distribution can be represented as a mixture of extreme points of the DFR class.

Original languageEnglish
Pages (from-to)303-310
Number of pages8
JournalProbability Theory and Related Fields
Volume57
Issue number3
DOIs
StatePublished - Sep 1981
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Mathematics (all)

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