The Bivariate Lack-of-Memory Distributions

Gwo Dong Lin Academia Sinica Xiaoling Dou Waseda University Satoshi Kuriki The Institute of Statistical Mathematics

Statistics Theory and Methods mathscidoc:2004.33001

Sankhya A, 81, (2), 273-297, 2019.12
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.
Lack-of-memory property, Bivariate lack-of-memory distributions, Marshall and Olkin’s BVE, Block and Basu’s BVE, Freund’s BVE, Likelihood ratio order, Usual stochastic order, Hazard rate order, Survival function, Copula, Survival copula, Positive quadrant dependent, Total positivity, Slepian’s lemma/inequality
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  title={The Bivariate Lack-of-Memory Distributions},
  author={Gwo Dong Lin, Xiaoling Dou, and Satoshi Kuriki},
  booktitle={Sankhya A},
Gwo Dong Lin, Xiaoling Dou, and Satoshi Kuriki. The Bivariate Lack-of-Memory Distributions. 2019. Vol. 81. In Sankhya A. pp.273-297.
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