A length-biased version of the Birnbaum-Saunders distribution with application in water quality
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.
KeywordsDiagnostics 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.
- Cook RD (1986) Assessment of local influence (with discussion). J R Stat Soc B 48:133–169Google Scholar
- Cook RD, Weisberg S (1982) Residuals and influence in regression. Chapman and Hall, LondonGoogle Scholar
- Gokhale S, Khare M (2003) Statistical methodologies and modelling in air pollution. J Inst Engineer India (Environ Engng Div) 83:46–53Google Scholar
- Johnson NL, Kotz S, Balakrishnan N (1995) Continuous univariate distributions—vol 2. Wiley, New YorkGoogle Scholar
- Leiva V, Hernández H, Riquelme M (2006) A new package for the Birnbaum-Saunders distribution. R News 6:35–40Google Scholar
- Leiva V, Barros M, Paula GA, Sanhueza A (2008) Generalized Birnbaum-Saunders distribution applied to air pollutant concentration. Environmetrics 19, doi: 10.1002/env.861 (in press)
- Patil GP (2002) Weighted distributions. In: El-Shaarawi AH, Piegorsch WW (eds) Encyclopedia of environmetrics, vol 4. Wiley, Chichester, pp 2369–2377Google Scholar