The Exponentiated Kumaraswamy-G Class: General Properties and Application

Ronaldo Silva; Frank Gomes-Silva; Manoel Ramos; Gauss Moutinho Cordeiro; Pedro Marinho; Thiago A. N. De Andrade

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The Exponentiated Kumaraswamy-G Class: General Properties and Application

Autores: Ronaldo Silva, Frank Gomes-Silva, Manoel Ramos, Gauss Moutinho Cordeiro, Pedro Marinho, Thiago A. N. De Andrade
Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 42, Nº. 1, 2019, págs. 1-33
Idioma: inglés
DOI: 10.15446/rce.v42n1.66205
Títulos paralelos:
- La clase Kumaraswamy-G exponenciada: propiedades generales y aplicación
Enlaces
- Texto completo
Resumen
- español
  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.
- English
  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.
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