Abstract

MARTINEZ-FLOREZ, GUILLERMO; MORENO-ARENAS, GERMÁN  and  VERGARA-CARDOZO, SANDRA. Properties and Inference for Proportional Hazard Models. Rev.Colomb.Estad. [online]. 2013, vol.36, n.1, pp.95-114. ISSN 0120-1751.

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.

Keywords : Hazard function; Kurtosis; Method of moments; Profile likelihood; Proportional hazard model; Skewness; Skew-normal distribution.

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