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A generalized modified Weibull distribution for lifetime modeling. (English) Zbl 1231.62015
Summary: 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 life time problems and reliability. The new distribution has a number of well-known life time 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.

MSC:
62E10 Characterization and structure theory of statistical distributions
62N05 Reliability and life testing
62F10 Point estimation
65C60 Computational problems in statistics (MSC2010)
Software:
Ox
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