Proportional reversed hazard and frailty models

Reversed hazard rates are found to be very useful in survival analysis and reliability especially in study on parallel systems and in the analysis of left censored lifetime data. In this paper, we derive a class of bivariate distributions having marginal proportional reversed hazard rates. We, then, introduce a class of proportional reversed hazard rates frailty models and propose a multivariate correlated gamma frailty model. Bivariate reversed hazard rates and association measure are discussed in terms of frailty parameters.