Multivariate Generalized Marshall–Olkin Distributions and Copulas



The multivariate generalized Marshall–Olkin distributions, which include the multivariate Marshall–Olkin exponential distribution due to Marshall and Olkin (J Am Stat Assoc 62:30–41, 1967) and multivariate Marshall–Olkin type distribution due to Muliere and Scarsini (Ann Inst Stat Math 39:429–441, 1987) as special cases, are studied in this paper. We derive the survival copula and the upper/lower orthant dependence coefficient, build the order of these survival copulas, and investigate the evolution of dependence of the residual life with respect to age. The main conclusions developed here are both nice extensions of the main results in Li (Commun Stat Theory Methods 37:1721–1733, 2008a, Methodol Comput Appl Probab 10:39–54, 2008b) and high dimensional generalizations of some results on the bivariate generalized Marshall–Olkin distributions in Li and Pellerey (J Multivar Anal 102:1399–1409, 2011).


IFR Marginal distribution NBU Proportional hazard PUOD Residual life Upper/lower orthant tail dependent 

AMS 2000 Subject Classifications

60E15 62H20 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamenChina

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