¹Universidad de Córdoba, Facultad de Ciencias, Departamento de Matemáticas y Estadística, Montería, Colombia. Professor. Email: gmartinez@correo.unicordoba.edu.co
²Universidad Industrial de Santander, Facultad de Ciencias, Escuela de Matemáticas, Bucaramanga, Colombia. Associate professor. Email: gmorenoa@uis.edu.co
³Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Bogotá, Colombia. Assistant Professor. Email: svergarac@unal.edu.co

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.

Key words: Hazard function, Kurtosis, Method of moments, Profile likelihood, Proportional hazard model, Skewness, Skew-normal distribution.

Consideramos una función de distribución continua arbitraria F(x) con función de densidad de probabilidad f(x)=dF(x)/dx y función de riesgo h_f(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 h_f(x). El modelo propuesto puede ajustar datos con alta asimetría o curtosis fuera del rango de cobertura permitido por la distribución normal, t-Student, logística, entre otras. Estimamos los parámetros del modelo usando máxima verosimilitud, verosimilitud perfilada y el método elemental de percentiles. Calculamos las matrices de información esperada y observada. Consideramos test de verosimilitudes para algunas hipótesis de interés en el modelo con función de riesgo proporcional a la distribución normal. Presentamos una aplicación con datos reales que ilustra que el modelo propuesto es adecuado.

Palabras clave: asimetría, curtosis, distribución skew-normal, función de riesgo, método de los momentos, modelo de riesgo proporcional, verosimilitud perfilada.

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