Properties and Inference for Proportional Hazard Models

We consider an arbitrary continuous cumulative distribution function F(x) with a probability density function f(x) = dF(x)/dx and hazard function h(f)(x) = f(x)/[1 - F(x)]. We propose a new family of distributions, the so-called proportional hazard distribution-function, whose hazard function is proportional to h(f)(x). The new model can fit data with high asymmetry or kurtosis outside the range covered by the normal, t-student and logistic distributions, among others. We estimate the parameters by maximum likelihood, profile likelihood and the elemental percentile method. The observed and expected information matrices are determined and likelihood tests for some hypotheses of interest are also considered in the proportional hazard normal distribution. We show an application to real data, which illustrates the adequacy of the proposed model.