Statistical Papers

, Volume 52, Issue 3, pp 591–619 | Cite as

The generalized inverse Weibull distribution

  • Felipe R. S. de Gusmão
  • Edwin M. M. OrtegaEmail author
  • Gauss M. Cordeiro
Regular Article


The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.


Censored data Data analysis Inverse Weibull distribution Maximum likelihood estimation Moment Weibull regression model 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Felipe R. S. de Gusmão
    • 1
  • Edwin M. M. Ortega
    • 2
    Email author
  • Gauss M. Cordeiro
    • 1
  1. 1.DEINFOUniversidade Federal Rural de PernambucoRecifeBrazil
  2. 2.Departamento de Ciências Exatas, ESALQUniversidade de São PauloPiracicabaBrazil

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