DOI: http://dx.doi.org/10.18273/revint.v35n1-2017004

Original article

Power Birnbaum-Saunders Student t distribution

Distribución Birnbaum-Saunders Potencia t de Student

 

Germán Moreno-Arenas¹

Guillermo Martínez-Flórez²

Heleno Bolfarin³

 

¹Universidad Industrial de Santander, Escuela de Matemáticas, Bucaramanga, Colombia.

²Universidad de Córdoba, Departamento de Matemáticas y Estadística, Montería, Colombia.

³Universidade de São Paulo, Departamento de Estatística, São Paulo, Brazil.

 

E-mail: gmorenoa@uis.edu.co

 

Abstract:

The fatigue life distribution proposed by Birnbaum and Saunders has been used quite effectively to model times to failure for materials subject to fatigue. In this article, we introduce an extension of the classical Birnbaum-Saunders distribution substituting the normal distribution by the power Student t distribution. The new distribution is more flexible than the classical Birnbaum-Saunders distribution in terms of asymmetry and kurtosis. We discuss maximum likelihood estimation of the model parameters and associated regression model. Two real data set are analysed and the results reveal that the proposed model better some other models proposed in the literature.

Keywords: Birnbaum-Saunders distribution, alpha-power distribution, power Student t distribution.

 

Resumen.

La distribución de probabilidad propuesta por Birnbaum y Saunders se ha usado con bastante eficacia para modelar tiempos de falla de materiales sujetos a la fátiga. En este artículo definimos una extensión de la distribución Birnbaum-Saunders clásica sustituyendo la distribución normal por la distribución potencia t de Student. La nueva distribución es más flexible que la distribución Birnbaum-Saunders clásica en términos de asimetría y curtosis. Presentamos los estimadores de máxima verosimilitud de los parámetros del modelo y su modelo de regresión asociado. El análisis de dos aplicaciones con datos reales revelan una superioridad del nuevo modelo con  relación a otros modelos existentes en la literatura

Palabras clave: Distribución Birnbaum-Saunders, distribución alfa potencia, distribución potencia t de Student

 

Received: 02 November 2015

Accepted: 26 May 2017.

 

Texto complete disponible en PDF

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To cite this article: G. Moreno-Arenas, G. Martínez-Flórez, H.  Bolfarine, Power Birnbaum-Saunders Student t distribution, Rev. Integr. Temas Mat. 35 (2017), No. 1, 51–70.