Published

2015-07-01

Slashed Exponentiated Rayleigh Distribution

Distribución Slash Rayleigh exponenciada

Keywords:

Exponentiated Rayleigh Distribution, Kurtosis, Maximum Likelihood, Rayleigh Distribution, Slash Distribution (en)
Curtosis, Distribución Rayleigh, Distribución Rayleigh exponenciada, Distribución Slash, Máxima verosimilitud. (es)

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Authors

  • Hugo S. Salinas Universidad de Atacama, Copiapó, Chile
  • Yuri A. Iriarte Instituto Tecnológico, Universidad de Atacama, Copiapó, Chile
  • Heleno Bolfarine IME, Universidad de Sao Paulo, Sao Paulo, Brasil

In this paper we introduce a new distribution for modeling positive data with high kurtosis. This distribution can be seen as an extension of the exponentiated Rayleigh distribution. This extension builds on the quotient of two independent random variables, one exponentiated Rayleigh in the numerator and Beta(q,1) in the denominator with q>0. It is called the slashed exponentiated Rayleigh random variable. There is evidence that the distribution of this new variable can be more flexible in terms of modeling the kurtosis regarding the exponentiated Rayleigh distribution. The properties of this distribution are studied and the parameter estimates are calculated using the maximum likelihood method. An application with real data reveals good performance of this new distribution.

En este trabajo presentamos una nueva distribución para modelizar datos positivos con alta curtosis. Esta distribución puede ser vista como una extensión de la distribución Rayleigh exponenciada. Esta extensión se construye en base al cuociente de dos variables aleatorias independientes, una Raileigh exponenciada en el numerador y una Beta(q; 1) en el denominador con q > 0. La llamaremos variable aleatoria slash Rayleigh exponenciada. Hay evidencias que la distribución de esta nueva variable puede ser más flexible en términos de modelizar la curtosis respecto a la distribución Rayleigh exponenciada. Se estudian las propiedades de esta distribución y se calculan las estimaciones de los parámetros utilizando el método de máxima verosimilitud. Una aplicación con datos reales revela el buen rendimiento de esta nueva distribución.

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