Properties and inference for proportional hazard models’, Revista Colombiana de Estadística

We consider an arbitrary continuous cumulative distribution function F (x) with a probability density function f(x) = dF (x)/dx and hazard func-tion hf (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 hf (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 like-lihood, 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