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An extended Birnbaum–Saunders model and its application in the study of environmental quality in Santiago, Chile

  • Filidor Vilca
  • Antonio Sanhueza
  • Víctor Leiva
  • George Christakos
Original Paper

Abstract

In this article, we introduce, characterize and apply an extended version of the Birnbaum–Saunders model based on the Mudolkar–Hutson skew distribution. This model is appropriated for describing phenomena involving accumulation of some type, as is the case of environmental contamination. Specifically, we find the density, distribution function, and moments of the new model. In addition, we derive several properties and transformations related to this distribution. Furthermore, we propose an estimation method for the parameters of the model. Moreover, we conduct a study of its hazard rate focuses in environmental analysis. A computational implementation in R language of the obtained results is discussed. Finally, we present two examples with real data from environmental quality in Chile that illustrate the proposed methodology.

Keywords

Hazard analysis Likelihood methods R software Skew distributions 

Notes

Acknowledgements

The authors wish to thank the referees for their helpful comments that greatly improved this article. This study was partially supported by a FAPESP grant from Brazil and by DIPUV 29-2006, FONDECYT 1080326, FONDECYT 1090265 and DIUFRO 080061 grants from Chile.

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Filidor Vilca
    • 1
  • Antonio Sanhueza
    • 2
  • Víctor Leiva
    • 3
  • George Christakos
    • 4
  1. 1.Departamento de EstatísticaUniversidade Estadual de CampinasSão PauloBrazil
  2. 2.Departamento de Matemática y EstadísticaUniversidad de La FronteraTemucoChile
  3. 3.Departamento de Estadística, CIMFAVUniversidad de ValparaísoValparaísoChile
  4. 4.Department of GeographySan Diego State UniversitySan DiegoUSA

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