The Bivariate Lack-of-Memory Distributions. (arXiv:1606.05097v1 [math.ST])3d
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由 Gwo Dong Lin, Xiaoling Dou, Satoshi Kuriki[url=][/url] 通过 Statistics authors/titles recent submissions[url=][/url]




We first review the univariate and bivariate lack-of-memory properties (LMPs). The univariate LMP is a remarkable characterization of the exponential distribution, while the bivariate LMP is shared by the famous Marshall and Olkin's, Block and Basu's as well as Freund's bivariate exponential distributions. 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 for 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 the BLM distributions.