The Bivariate Lack-of-Memory Distributions

Gwo Dong Lin, Xiaoling Dou, Satoshi Kuriki

    Research output: Contribution to journalArticle

    1 Citation (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)1-25
    Number of pages25
    JournalSankhya A
    DOIs
    Publication statusAccepted/In press - 2017 Dec 15

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    Keywords

    • 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
    • Slepian’s lemma/inequality
    • Survival copula
    • Survival function
    • Total positivity
    • Usual stochastic order

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Statistics and Probability

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