English

The Bivariate Lack-of-Memory Distributions

Statistics Theory 2017-12-19 v5 Statistics Theory

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.

Keywords

Cite

@article{arxiv.1606.05097,
  title  = {The Bivariate Lack-of-Memory Distributions},
  author = {Gwo Dong Lin and Xiaoling Dou and Satoshi Kuriki},
  journal= {arXiv preprint arXiv:1606.05097},
  year   = {2017}
}
R2 v1 2026-06-22T14:26:45.798Z