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Revista Colombiana de Estadística

versão impressa ISSN 0120-1751

Rev.Colomb.Estad. vol.42 no.1 Bogotá jan./jun. 2019  Epub 23-Maio-2019

http://dx.doi.org/10.15446/rce.v42n1.66205 

Artículos originales de investigación

The Exponentiated Kumaraswamy-G Class: General Properties and Application

La clase Kumaraswamy-G exponenciada: propiedades generales y aplicación

Ronaldo Silvaa  , Frank Gomes-Silvab  , Manoel Ramosc  , Gauss Cordeirod  , Pedro Marinhoe  , Thiago A. N. De Andradef 

a Recife Military School, Recife, Brazil. ronaldovenanciorvs@gmail.com

b Department of Statistics and Informatics, Federal Rural University of Pernambuco, Recife, Brazil. franksinatrags@gmail.com

c Federal Institute of Paraíba, João Pessoa, Brazil. wallace.ifpb@gmail.com

d Department of Statistics, Federal University of Pernambuco, Recife, Brazil. gauss@de.ufpe.br

e Department of Statistics, Federal University of Paraíba, João Pessoa, Brazil. pedro.rafael.marinho@gmail.com

f Department of Statistics, Federal University of Pernambuco, Recife, Brazil. thiagoan.andrade@gmail.com

Abstract

We propose a new family of distributions called the exponentiated Kumaraswamy-G class with three extra positive parameters, which generalizes the Cordeiro and de Castro's family. Some special distributions in the new class are discussed. We derive some mathematical properties of the proposed class including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, mean deviations, reliability, Rényi entropy and Shannon entropy. The method of maximum likelihood is used to fit the distributions in the proposed class. Simulations are performed in order to assess the asymptotic behavior of the maximum likelihood estimates. We illustrate its potentiality with applications to two real data sets which show that the extended Weibull model in the new class provides a better fit than other generalized Weibull distributions.

Key words: BFGS method; Exponential distribution; Exponentiated Kumaraswamy-G; Kumaraswamy distribution; Maximum likelihood estimation

Resumen

Proponemos una nueva clase de distribuciones llamada la clase de Kumaraswamy-G exponenciada con tres parámetros positivos adicionales, que generaliza la familia de Cordeiro y de Castro. Se discuten algunas distribuciones especiales en la nueva clase. Derivamos algunas propiedades matemáticas de la clase propuesta, incluyendo expresiones explícitas para la función cuartil, momentos ordinarios e incompletos, función generadora, desviaciones medias, confiabilidad, entropía de Rényi y entropía de Shannon. El método de máxima verosimilitud se utiliza para ajustar las distribuciones en la clase propuesta. Se realizaron simulaciones para evaluar el comportamiento asintótico de las estimaciones de máxima verosimilitud. Ilustramos su potencialidad con dos aplicaciones a dos conjuntos de datos reales que muestra que el modelo extendido de Weibull en la nueva clase proporciona un mejor ajuste que otras distribuciones generalizadas de Weibull.

Palabras-clave: Distribución exponencial; Distribución Kumaraswamy; Estimación de máxima verosimilitud; Kumaraswamy-G Exponenciada; Método BFGS

Full text available only in PDF format.

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