Multivariate distributions with proportional reversed hazard marginals

Abstract

Several univariate proportional reversed hazard models have been proposed in the literature. Recently, Kundu and Gupta (2010) proposed a class of bivariate models with proportional reversed hazard marginals. It is observed that the proposed bivariate proportional reversed hazard models have a singular component. In this paper we introduce the multivariate proportional reversed hazard models along the same manner. Moreover, it is observed that the proposed multivariate proportional reversed hazard model can be obtained from the Marshall–Olkin copula. The multivariate proportional reversed hazard models also have a singular component, and their marginals have proportional reversed hazard distributions. The multivariate ageing and the dependence properties are discussed in details. We further provide some dependence measure specifically for the bivariate case. The maximum likelihood estimators of the unknown parameters cannot be expressed in explicit forms. We propose to use the EM algorithm to compute the maximum likelihood estimators. One trivariate data set has been analysed for illustrative purposes.