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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bain, L. J. and Antle, C. E. (1967). Estimation of parameters in the Weibull distribution, Technometrics, 9, 621–627.
Bayerisches Landesamt für Wasserwirtschaft München, Deutsche gewässerkundliche Jahrbücher 1941–1990, Donaugebiet, Bayerische Landesstelle für Gewässerkunde, München.
Bayerisches Staatsministerium für Landesentwicklung und Umweltfragen (1995), Umwelt & Entwicklung Bayern 6/95: Hochwasser hausgemacht? München.
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.
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.
Cheng, R. C. and Taylor, L. (1995). Non-regular maximum likelihood problems, Journal of the Royal Statistical Society, B, 57, 3–44.
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.
Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events, Berlin: Springer-Verlag.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994). Distributions in Statistics: Continuous Univariate Distributions, I, New York: John Wiley & Sons.
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.
Offinger, R. (1996). Schätzer in dreiparametrigen Weibull-Modellen und Untersuchung ihrer Eigenschaften mittels Simulation, Diplomarbeit, Universität Augsburg.
Scales, L. E. (1985). Introduction to Non-Linear Optimization London: Macmillan.
Scholz, F. W. (1980). Towards a unified definition of maximum likelihood, The Canadian Journal of Statistics, 8, 193–203.
Witting, H. and Müller-Funk, U. (1995). Mathematische Statistik II: Parametrische Modelle und nichtparametrische Funktionale, Stuttgart: Teubner.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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