¹Universidade Federal de Pernambuco, Centro de Ciências Exatas e da Natureza, Departamento de Estatística, Recife, Brasil. Graduate student. Email: thiagoan.andrade@gmail.com
²Universidade Federal de Pernambuco, Centro de Ciências Exatas e da Natureza, Departamento de Estatística, Recife, Brasil. Graduate student. Email: heloisa.mrodrigues@ufpe.br
³Universidade Federal do Piauí, Centro de Ciências da Natureza, Departamento de Estatística, Teresina, Brasil. Assistent Professor. Email: m.p.bourguignon@gmail.com
⁴Universidade Federal de Pernambuco, Centro de Ciências Exatas e da Natureza, Departamento de Estatística, Recife, Brasil. Professor. Email: gauss@de.ufpe.br

A class of univariate distributions called the exponentiated generalized class was recently proposed in the literature. A four-parameter model within this class named the exponentiated generalized Gumbel distribution is defined. We discuss the shapes of its density function and obtain explicit expressions for the ordinary moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves and Rényi entropy. The density function of the order statistic is derived. The method of maximum likelihood is used to estimate model parameters. We determine the observed information matrix. We provide a Monte Carlo simulation study to evaluate the maximum likelihood estimates of model parameters and two applications to real data to illustrate the importance of the new model.

Key words: Gumbel Distribution, Maximum Likelihood, Moment, Rényi Entropy.

Recientemente fue propuesta una clase de distribuciones univariadas conocida como la clase exponencializada generalizada. Dentro de esta clase se define un modelo con cuatro parámetros conocido como distribución Gumbel exponencializada generalizada. En este artículo estudiamos las formas de la función de densidad de este modelo, obtenemos expresiones explicitas para los momentos ordinarios, las funciones generadora de momentos y cuantílica, para los desvíos medios, las curvas de Bonferroni y Lorenz, y, para la entropía de Rényi. Derivamos la función de densidad de la estadística de orden. Usamos el método de máxima verosimilitud para estimar los parámetros del modelo. Determinamos la matriz de información observada. Presentamos una simulación de Monte Carlo que evalúa las estimativas de máxima verosimilitud de los parámetros del modelo y presentamos dos aplicaciones a datos reales que ilustran la importancia del modelo nuevo.

Palabras clave: distribución Gumbel, entropía de Rényi, máxima verosimilitud, momentos.

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