The Marshall-Olkin extended Weibull family of distributions

We introduce a new class of models called the Marshall-Olkin extended Weibull family of distributions based on the work by Marshall and Olkin (Biometrika 84:641–652, 1997). The proposed family includes as special cases several models studied in the literature such as the Marshall-Olkin Weibull, Mars...

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Detalles Bibliográficos
Autores: Santos-Neto, Manoel, Bourguignon, Marcelo, Zea, Luz M., Nascimento, Abraão DC, Cordeiro, Gauss M.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:Brasil
Institución:Universidade Federal do Rio Grande do Norte (UFRN)
Repositorio:Repositório Institucional da UFRN
Idioma:inglés
OAI Identifier:oai:repositorio.ufrn.br:123456789/49653
Acceso en línea:https://repositorio.ufrn.br/handle/123456789/49653
Access Level:acceso abierto
Palabra clave:Extended Weibull distribution
Hazard rate function
Marshall-Olkin distribution
Maximum likelihood estimation
Survival function
Descripción
Sumario:We introduce a new class of models called the Marshall-Olkin extended Weibull family of distributions based on the work by Marshall and Olkin (Biometrika 84:641–652, 1997). The proposed family includes as special cases several models studied in the literature such as the Marshall-Olkin Weibull, Marshall-Olkin Lomax, Marshal-Olkin Fréchet and Marshall-Olkin Burr XII distributions, among others. It defines at least twenty-one special models and thirteen of them are new ones. We study some of its structural properties including moments, generating function, mean deviations and entropy. We obtain the density function of the order statistics and their moments. Special distributions are investigated in some details. We derive two classes of entropy and one class of divergence measures which can be interpreted as new goodness-of-fit quantities. The method of maximum likelihood for estimating the model parameters is discussed for uncensored and multi-censored data. We perform a simulation study using Markov Chain Monte Carlo method in order to establish the accuracy of these estimators. The usefulness of the new family is illustrated by means of two real data sets.