A length-biased version of the Birnbaum-Saunders distribution with application in water quality

  • Víctor LeivaEmail author
  • Antonio Sanhueza
  • José M. Angulo
Original Paper


In this article, we develop a new model based on the Birnbaum-Saunders distribution that results to be both useful and practical for environmental sciences. The density, distribution and hazard functions, moments and properties of this new model are presented. A graphical analysis of the density is also provided. Furthermore, we estimate parameters, propose asymptotic inference and discuss influence diagnostics by using likelihood methods for the new distribution. An illustrative example with real data related to water quality indicates the adequacy on the new distribution.


Diagnostics Likelihood methods Skewed distributions Water quality 



The authors wish to thank the Editor, AE and referees for their helpful comments that aided in improving this article. Also, the authors thank the Dirección General de Aguas of the government of Chile for providing the data used in this article. This research was partially supported by grants FONDECYT 1050862, Chile, International Clinical Epidemiology Network (INCLEN) and DGI MTM2005-08597 and Andalusian CICYE P05-FQM-00990, Spain.


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Víctor Leiva
    • 1
    Email author
  • Antonio Sanhueza
    • 2
  • José M. Angulo
    • 3
  1. 1.Departamento de EstadísticaUniversidad de ValparaísoValparaísoChile
  2. 2.Departamento de Matemática y EstadísticaUniversidad de La FronteraTemucoChile
  3. 3.Departamento de Estadística e Investigación OperativaUniversidad de GranadaGranadaSpain

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