A generalized modified Weibull distribution for lifetime modeling

Authors:
Jalmar M. F. Carrasco;Edwin M. M. Ortega;Gauss M. Cordeiro
Affiliations:
ESALQ, Universidade de São Paulo, Piracicaba, Brazil;ESALQ, Universidade de São Paulo, Piracicaba, Brazil;DEINFO, Universidade Federal Rural de Pernambuco, Brazil
Venue:
Computational Statistics & Data Analysis
Year:
2008

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Abstract

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution.