Classes of discrete lifetime distributions

A W Kemp

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

Abstract

Several results that characterize the distribution of a lifetime variable. T, with probability mass function (pmf) p,, where t = 0, 1, 2, ..., by its survivor function, S-t = Sigma(jgreater than or equal tot)p(j) its hazard function. h(t) = p(t)/S-t, its cumulative hazard function, Lambda(t) = - ln S-t, its accumulated hazard function, H-t = Sigma(j=0)(t) h(t), and its mean residual life function, L-T = E[(T - t)\T greater than or equal to t] (an initially faulty item is deemed to have a zero lifetime), are presented. These include results that have previously appeared in the literature as well as some new results. Differences in the terminology used by engineers. actuaries. and biostatisticians are pointed out and clarified. Attention is focussed on the relationships between the IFR/DFR, IFRA/DFRA, NBU/NWU. NBUE/NWUE, and IMRL/DMLR classes to which a discrete lifetime distribution and its current age distribution belong.

Original languageEnglish
Pages (from-to)3069-3093
Number of pages25
JournalCommunications in Statistics: Theory and Methods
Volume33
DOIs
Publication statusPublished - 2004

Keywords

  • reliability
  • characterizations
  • discrete distributions
  • survivor function
  • failure rate
  • hazard function
  • cumulative hazard function
  • accumulated hazard function
  • mean residual life function
  • logconvexity
  • logconcavity
  • current age distribution
  • TIME

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