Dependence properties of multivariate distributions with proportional hazard rate marginals

Abstract

• Dependence properties related to survival and survival copula function. • Trivariate dependence measure coefficient. • Multivariate lower and upper orthant tail dependence coefficient. • Density of the singular copula function. • Application in medicine. In this paper, we introduce a new family of multivariate distributions , so called the multivariate proportional hazard rate family of distributions and study its properties. We derive multivariate dependence properties based on a survival function and based on a survival copula function. Multivariate dependence properties based on a survival function are given by multivariate total positivity of order 2, right corner set increasing, smaller in lower orthant order and right tail increasing. Multivariate dependence properties based on a survival copula function are some coefficients of concordance. The survival copula function is used to model this family of multivariate distributions. We illustrate capability of the introduced model on a real data set related to the level of thyroid hormone.