The Bivariate Lack-of-Memory Distributions

Gwo Dong Lin*, Xiaoling Dou, Satoshi Kuriki

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We treat all the bivariate lack-of-memory (BLM) distributions in a unified approach and develop some new general properties of the BLM distributions, including joint moment generating function, product moments, and dependence structure. Necessary and sufficient conditions for the survival functions of BLM distributions to be totally positive of order two are given. Some previous results about specific BLM distributions are improved. In particular, we show that both the Marshall–Olkin survival copula and survival function are totally positive of all orders, regardless of parameters. Besides, we point out that Slepian’s inequality also holds true for BLM distributions.

Original languageEnglish
Pages (from-to)273-297
Number of pages25
JournalSankhya A
Volume81
Issue number2
DOIs
Publication statusPublished - 2019 Dec 1

Keywords

  • 62H05
  • 62H20
  • 62N86
  • Bivariate lack-of-memory distributions
  • Block and Basu’s BVE
  • Copula
  • Freund’s BVE
  • Hazard rate order
  • Lack-of-memory property
  • Likelihood ratio order
  • Marshall and Olkin’s BVE
  • Positive quadrant dependent
  • Primary: 62N05
  • Slepian’s lemma/inequality
  • Survival copula
  • Survival function
  • Total positivity
  • Usual stochastic order

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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