# Properties and inference for proportional hazard models

We consider an arbitrary continuous cumulative distribution functionFx with a probability density function fx = dFx=dx and hazard functionhf x = fx=1

Tipo de documento: Artículo - Article

Palabras clave: Hazard function, Kurtosis, Method of moments, Profile likelihood, Proportional hazard model, Skewness, Skew-normal distribution

Source: http://www.bdigital.unal.edu.co

## Teaser

Revista Colombiana de Estadística Junio 2013, volumen 36, no.
1, pp.
95 a 114 Properties and Inference for Proportional Hazard Models Propiedades e inferencia para modelos de Hazard proporcional Guillermo Martínez-Florez1,a , Germán Moreno-Arenas2,b , Sandra Vergara-Cardozo3,c 1 Departamento 2 Escuela de Matemáticas y Estadística, Facultad de Ciencias, Universidad de Córdoba, Montería, Colombia de Matemáticas, Facultad de Ciencias, Universidad Industrial de Santander, Bucaramanga, Colombia 3 Departamento de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá, Colombia Abstract We consider an arbitrary continuous cumulative distribution function F (x) with a probability density function f (x) = dF (x)-dx and hazard function 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 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. Key words: Hazard function, Kurtosis, Method of moments, Profile likelihood, Proportional hazard model, Skewness, Skew-normal distribution. Resumen Consideramos una función de distribución continua arbitraria F (x) con función de densidad de probabilidad f (x) = dF (x)-dx y función de riesgo hf (x) = f (x)-[1 − F (x)].
En este artículo proponemos una nueva familia de distribuciones cuya función de riesgo es proporcional a la función de riesgo hf (x).
El modelo propuesto puede ajustar datos con alta asim...