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Improved Shape Parameter Estimation in a Discrete Weibull Model

  • P. Araújo Santos
  • M. I. Fraga Alves
Chapter
Part of the Studies in Theoretical and Applied Statistics book series (STAS)

Abstract

A new shape parameter estimator for a discrete Weibull model is proposed. This estimator is based on an extension of the Khan et al. (IEEE Trans. Reliab. 38:348–350, 1989) method of proportions. Simulations are carried out to illustrate the improvement achieved in terms of bias and mean square error. The proposed estimator is applied on a financial dataset dealing with durations between violations in a quantitative risk management environment.

Keywords

Moment Estimator Duration Dependence Empirical Cumulative Distribution Function Increase Failure Rate Approximate Maximum Likelihood 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This research was partially supported by Fundação para a Ciência e Tecnologia (FCT/PROTEC, FCT/OE and PTDC/FEDER) and Center of Statistics and Applications of University of Lisbon (CEAUL).

References

  1. 1.
    Christoffersen, P.: Evaluating intervals forecasts. Int. Econ. Rev. 39, 841–862 (1998)Google Scholar
  2. 2.
    Bracquemond, C., Gaudoin, O.: A survey on discrete lifetime distributions. Int. J. Reliab. Qual. Safe. Eng. 10, 69–98 (2003)Google Scholar
  3. 3.
    Harman, Y.S., Zuehlke, T.W.: Duration dependence testing for speculative bubbles. J. Econ. Finance 28, 17–36 (2004)Google Scholar
  4. 4.
    Haas, M.: Improved duration-based backtesting of Value-at-Risk. J. Risk 8, 17–36 (2005)Google Scholar
  5. 5.
    Jazi, M.A., Lai, C., Alamatsaz, M.H.: A discrete inverse Weibull distribution and estimation of its parameters. Stat. Methodol. 7, 121–132 (2010)Google Scholar
  6. 6.
    Lin, T., Guillén, M.: The rising hazards of party incumbency. A discrete renewal analysis. Polit. Anal. 7, 31–57 (1998); An Annual Pulication of the Methodology Section of the American Political Science AssociationGoogle Scholar
  7. 7.
    Lancaster, T.: Econometric methods for the duration of unemployment. Econometrica 47, 939–956 (1979)Google Scholar
  8. 8.
    Padgett, W.J., Spurrier, J.D.: Discrete failure models. IEEE Trans. Reliab. 34, 253–256 (1985)Google Scholar
  9. 9.
    Khan, M.S.A., Khalique, A., Abouammoh, A.M.: On estimating parameters in a discrete weibull distribution. IEEE Trans. Reliab. 38, 348–350 (1989)Google Scholar
  10. 10.
    Kulasekera, K.B.: Approximate MLE’s of the parameters of a discrete weibull distribution with Type I censored data. Microelectron. Reliab. 34, 1185–1188 (1994)Google Scholar
  11. 11.
    Nakagawa, T., Osaki, S.: The discrete Weibull distribution. IEEE Trans. Reliab. 24, 300–301 (1975)Google Scholar
  12. 12.
    Stein, W.E., Dattero, R.: A new discrete Weibull distribution. IEEE Trans. Reliab. R-33, 196–197 (1984)Google Scholar
  13. 13.
    R Development Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. http://www.R-project.org (2008)

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Instituto Politécnico de Santarém, Departamento de Informática e Métodos QuantitativosEscola Superior de Gestão e TecnologiaSantarémPortugal
  2. 2.Faculdade de Ciências, Departamento de Estatística e Investigação OperacionalUniversidade de LisboaLisboaPortugal

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