Properties and Inference for Proportional Hazard Models

Abstract

We consider an arbitrary continuous cumulative distribution functionF(x) with a probability density function f(x) = dF(x)=dx and hazard functionhf (x) = f(x)=[1F(x)]: We propose a new family of distributions, theso-called proportional hazard distribution-function, whose hazard functionis proportional to hf (x). The new model can fit data with high asymmetryor kurtosis outside the range covered by the normal, t-student and logisticdistributions, among others. We estimate the parameters by maximum likelihood,profile likelihood and the elemental percentile method. The observedand expected information matrices are determined and likelihood tests forsome hypotheses of interest are also considered in the proportional hazardnormal distribution. We show an application to real data, which illustratesthe adequacy of the proposed model.