On maximum likelihood estimates of a proportional hazard rate model parameters based on record values

Abstract

The proportional hazard rate models have wide acceptance in modeling complex data from different engineering, reliability, and survival applications. The hazard rate function of such models is able to model data with a monotonic or a bathtub-shape hazard rate. In this paper, we propose a subclass of proportional hazard rate models with three-parameters for which we have proved the existence and uniqueness of the maximum likelihood estimators based on upper kth record values. The proposed inference is found especially useful in some real illustrations within mechanical and medical analysis. Finally, several remarks are presented in the final stage of this paper.