2016/06/30 by Gwo Dong Lin, Xiaoling Dou, Satoshi Kuriki · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #Bivariate analysis #Copula (linguistics) #Financial Risk and Volatility Modeling #Joint probability distribution #Marginal distribution #Moment (physics) #Probability distribution #Product (mathematics) #Statistical Distribution Estimation and Applications #Survival function #math.ST #msc:62H05 #msc:62H20 #msc:62N05 #msc:62N86 #stat.TH
paper · pdf · doi:10.1007/s13171-017-0119-1
published as Sankhya Series A, 2017, Vol. 79
openalex created_date 2016/06/24 · openalex publication_date 2017/12/15 · arxiv created 2017/12/16 · arxiv updated 2017/12/19 · openalex updated_date 2026/08/05
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.