@article{d1c41178debe4a53afba18303d55a79c,
title = "The Bivariate Lack-of-Memory Distributions",
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{\textquoteright}s inequality also holds true for BLM distributions.",
keywords = "62H05, 62H20, 62N86, Bivariate lack-of-memory distributions, Block and Basu{\textquoteright}s BVE, Copula, Freund{\textquoteright}s BVE, Hazard rate order, Lack-of-memory property, Likelihood ratio order, Marshall and Olkin{\textquoteright}s BVE, Positive quadrant dependent, Primary: 62N05, Slepian{\textquoteright}s lemma/inequality, Survival copula, Survival function, Total positivity, Usual stochastic order",
author = "Lin, {Gwo Dong} and Xiaoling Dou and Satoshi Kuriki",
note = "Funding Information: The authors would like to thank the Editor-in-Chief and two referees for helpful comments and constructive suggestions which improve the presentation of the paper. The paper was presented at the Ibusuki International Seminar, Ibusuki Phoenix Hotel, held from 6th to 8th March 2016 by Waseda University, Japan. The authors thank the organizer Professor Masanobu Taniguchi for his kind invitation and the audiences for their comments and suggestions. Publisher Copyright: {\textcopyright} 2017, Indian Statistical Institute.",
year = "2019",
month = dec,
day = "1",
doi = "10.1007/s13171-017-0119-1",
language = "English",
volume = "81",
pages = "273--297",
journal = "Sankhya A",
issn = "0976-836X",
publisher = "Springer India",
number = "2",
}