The beta exponentiated Weibull distribution

作者：Cordeiro Gauss M; Gomes Antonio Eduardo; da Silva Cibele Queiroz; Ortega Edwin M M^*

来源：Journal of Statistical Computation and Simulation, 2013, 83(1): 114-138.

DOI：10.1080/00949655.2011.615838

• beta exponentiated Weibull distribution
• beta Weibull distribution
• exponentiated Weibull distribution
• information matrix
• maximum likelihood
• moment-generating function
• Weibull distribution

The Weibull distribution is one of the most important distributions in reliability. For the first time, we introduce the beta exponentiated Weibull distribution which extends recent models by Lee et al. [Beta-Weibull distribution: some properties and applications to censored data, J. Mod. Appl. Statist. Meth. 6 (2007), pp. 173186] and Barreto-Souza et al. [The beta generalized exponential distribution, J. Statist. Comput. Simul. 80 (2010), pp. 159172]. The new distribution is an important competitive model to the Weibull, exponentiated exponential, exponentiated Weibull, beta exponential and beta Weibull distributions since it contains all these models as special cases. We demonstrate that the density of the new distribution can be expressed as a linear combination of Weibull densities. We provide the moments and two closed-form expressions for the moment-generating function. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The density of the order statistics can also be expressed as a linear combination of Weibull densities. We obtain the moments of the order statistics. The expected information matrix is derived. We define a log-beta exponentiated Weibull regression model to analyse censored data. The estimation of the parameters is approached by the method of maximum likelihood. The usefulness of the new distribution to analyse positive data is illustrated in two real data sets.

• 出版日期2013-1-1