Statistical Methods & Applications

, Volume 21, Issue 2, pp 139–168 | Cite as

The Kumaraswamy Gumbel distribution

  • Gauss M. Cordeiro
  • Saralees NadarajahEmail author
  • Edwin M. M. Ortega


The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. We propose a generalization—referred to as the Kumaraswamy Gumbel distribution—and provide a comprehensive treatment of its structural properties. We obtain the analytical shapes of the density and hazard rate functions. We calculate explicit expressions for the moments and generating function. The variation of the skewness and kurtosis measures is examined and the asymptotic distribution of the extreme values is investigated. Explicit expressions are also derived for the moments of order statistics. The methods of maximum likelihood and parametric bootstrap and a Bayesian procedure are proposed for estimating the model parameters. We obtain the expected information matrix. An application of the new model to a real dataset illustrates the potentiality of the proposed model. Two bivariate generalizations of the model are proposed.


Beta distribution Gumbel distribution Information matrix Kumaraswamy distribution Maximum likelihood Order statistic 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Gauss M. Cordeiro
    • 1
  • Saralees Nadarajah
    • 2
    Email author
  • Edwin M. M. Ortega
    • 3
  1. 1.Departamento de EstatísticaUniversidade Federal de PernambucoRecifeBrazil
  2. 2.School of MathematicsUniversity of ManchesterManchesterUK
  3. 3.Departamento de Ciências ExatasUniversidade de São PauloPiracicabaBrazil

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