Skip to main content

Least Squares and Minimum Distance Estimation in the Three-Parameter Weibull and Fréchet Models with Applications to River Drain Data

  • Chapter
  • 398 Accesses

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

After introducing three-Parameter Weibull and Fréchet models we define various least squares and minimum distance estimation methods in general. We then show how these methods can be applied to the Weibull and Fréchet models and examine the quality of two special estimators in a small simulation study. These studies show that the estimators are a good alternative to already known estimators. Finally we discuss the application of the models to river drain data and some involved problems.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bain, L. J. and Antle, C. E. (1967). Estimation of parameters in the Weibull distribution, Technometrics, 9, 621–627.

    Article  MathSciNet  MATH  Google Scholar 

  2. Bayerisches Landesamt für Wasserwirtschaft München, Deutsche gewässerkundliche Jahrbücher 1941–1990, Donaugebiet, Bayerische Landesstelle für Gewässerkunde, München.

    Google Scholar 

  3. Bayerisches Staatsministerium für Landesentwicklung und Umweltfragen (1995), Umwelt & Entwicklung Bayern 6/95: Hochwasser hausgemacht? München.

    Google Scholar 

  4. Carmody, T. J., Eubank, R. L. and LaRiccia, V. N. (1984), A family of minimum quantile distance estimators for the three-parameter Weibull distribution Statistische Hefte, 25, 69–82.

    Article  MATH  Google Scholar 

  5. Castillo, E. (1994). Extremes in engineering applications, In Extreme Value Theory and Applications, Proceedings of the Conference on Extreme Value Theory and Applications, Vol. 1 (Eds., J. Galambos, J. Lechner and E. Simiu), Gaithersburg, Maryland 1993, pp. 15–42, Dordrecht: Kluwer.

    Google Scholar 

  6. Cheng, R. C. and Taylor, L. (1995). Non-regular maximum likelihood problems, Journal of the Royal Statistical Society, B, 57, 3–44.

    MATH  Google Scholar 

  7. Cohen, A. C., Whitten, B. J. and Ding, Y. (1984). Modified moment estimation for the three-parameter Weibull distribution, Journal of Quality Technology, 16, 159–167.

    Google Scholar 

  8. Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events, Berlin: Springer-Verlag.

    MATH  Google Scholar 

  9. Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994). Distributions in Statistics: Continuous Univariate Distributions, I, New York: John Wiley & Sons.

    Google Scholar 

  10. Lockhart, R. A. and Stephens, M. A. (1994). Estimation and tests of fit for the three-parameter Weibull distribution, Journal of the Royal Statistical Society B, 56, 491–500.

    MathSciNet  MATH  Google Scholar 

  11. Offinger, R. (1996). Schätzer in dreiparametrigen Weibull-Modellen und Untersuchung ihrer Eigenschaften mittels Simulation, Diplomarbeit, Universität Augsburg.

    Google Scholar 

  12. Scales, L. E. (1985). Introduction to Non-Linear Optimization London: Macmillan.

    Google Scholar 

  13. Scholz, F. W. (1980). Towards a unified definition of maximum likelihood, The Canadian Journal of Statistics, 8, 193–203.

    Article  MathSciNet  MATH  Google Scholar 

  14. Witting, H. and Müller-Funk, U. (1995). Mathematische Statistik II: Parametrische Modelle und nichtparametrische Funktionale, Stuttgart: Teubner.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Birkhäuser Boston

About this chapter

Cite this chapter

Offinger, R. (1998). Least Squares and Minimum Distance Estimation in the Three-Parameter Weibull and Fréchet Models with Applications to River Drain Data. In: Kahle, W., von Collani, E., Franz, J., Jensen, U. (eds) Advances in Stochastic Models for Reliability, Quality and Safety. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2234-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2234-7_6

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7466-7

  • Online ISBN: 978-1-4612-2234-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics