Lifetime Data Analysis

, Volume 16, Issue 3, pp 409–430 | Cite as

The beta modified Weibull distribution

  • Giovana O. Silva
  • Edwin M. M. OrtegaEmail author
  • Gauss M. Cordeiro


A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.


Beta distribution Exponentiated exponential Exponentiated Weibull Generalized modified Weibull Maximum likelihood Modified Weibull Observed information matrix Weibull distribution 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Giovana O. Silva
    • 1
  • Edwin M. M. Ortega
    • 1
    Email author
  • Gauss M. Cordeiro
    • 2
  1. 1.ESALQUniversidade de São PauloPiracicabaBrazil
  2. 2.DEINFOUniversidade Federal Rural de PernambucoRecifeBrazil

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