Reverse hazard

Abstract

As a dual of the hazard rate function, reversed hazard rate characterizes the probability of an immediate past failure, given that a failure has already occurred. This function appears to be important both in survival and reliability studies as it complements a thorough understanding of the failure behavior of the underlying stochastic system. In this article, we provide the basic notions regarding reverse hazard rate function, and compare and contrast its properties with the hazard rate function. We further point to the extension of the concept to bivariate case. The estimation of the distribution function via the reverse hazard rate is also briefly discussed in the context of right truncated data.