TY - JOUR
T1 - Multivariate Generalized Marshall-Olkin Distributions and Copulas
AU - Lin, Jianhua
AU - Li, Xiaohu
PY - 2014/3
Y1 - 2014/3
N2 - 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).
AB - 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).
KW - IFR
KW - Marginal distribution
KW - NBU
KW - PUOD
KW - Proportional hazard
KW - Residual life
KW - Upper/lower orthant tail dependent
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U2 - 10.1007/s11009-012-9297-4
DO - 10.1007/s11009-012-9297-4
M3 - Article
AN - SCOPUS:84894642840
SN - 1387-5841
VL - 16
SP - 53
EP - 78
JO - Methodology and Computing in Applied Probability
JF - Methodology and Computing in Applied Probability
IS - 1
ER -