Abstract
In this chapter we develop the model which represents the cornerstone of extreme value theory.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Further Reading
Fisher, R. A., and Tippett, L. H. C. (1928). On the estimation of the frequency distributions of the largest or smallest member of a sample. Proceedings of the Cambridge Philosophical Society 24, 180–190.
Gumbel, E. J. (1958). Statistics of Extremes. Columbia University Press, New York.
Von Mises, R. (1954). La distribution de la plus grande de n valeurs. In Selected Papers, Volume II, pages 271–294. American Mathematical Society, Providence, RI.
Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of meteorological events. Quarterly Journal of the Royal Meteorological Society 81, 158–172.
Prescott, P. D Walden, A. T. (1983). Maximum likelihood estimation of the parameters of the three-parameter generalized extreme value distribution from censored samples. Journal of Statistical Computation and Simulation 16, 241–250.
Hosking, J. R. M. (1985). Maximum likelihood estimation of the parameters of the generalized extreme value distribution. Applied Statistics 34, 301–310.
Smith, R. L. (1985). Maximum likelihood estimation in a class of non-regular cases. Biometrika 72, 67–90.
Hosking, J. R. M. (1984). Testing whether the shape parameter is zero in the generalized extreme value distribution. Biometrika 71, 367–374.
Hall, P., and Tajvidi, N. (2000a). Distribution and dependence function estimation for bivariate extreme value distributions. Bernoulli 6, 835–844.
Cohen, J. P. (1988). Fitting extreme value distributions to maxima. Sankyha, Series A 50, 74–97.
Smith, R. L. (1995). Likelihood and modified likelihood estimation for distributions with unknown endpoints. In Balakrishnan, N., editor, Recent Advances in Life-Testing and Reliabilty. A Volume in Honor of Alonzo Clifford Cohen, Jr., chapter 24, pages 455–474. Crc Press, Boca Raton.
Buishand, T. A. (1989). Statistics of extremes in climatology.Statistica Neerlandica 43 1–30.
Carter, D. J. T., and Challenor, P. G. (1981). Estimating return values of environmental parameters. Quarterly Journal of the Royal Meteorological Society 107, 259–266.
DE Haan, L. (1990). Fighting the arch-enemy with mathematics. Statistica Neerlandica 44, 45–68.
Dixon, M. J., and Tawn, J. A. (1999). The effect of non-stationarity on extreme sea-level estimation. Applied Statistics 48, 135–151.
Robinson, M. E., and Tawn, J. A. (1997). Statistics for extreme sea currents. Applied Statistics 46, 183–205.
Zwiers, F. W. (1987). An extreme value analysis of wind speeds at 5 Canadian locations. Journal of the Canadian Statistical Society 15, 317–327.
Walshaw, D. (2000). Modelling extreme wind speeds in regions prone to hurricanes. Applied Statistics 49, 51–62.
Henery, R. J. (1984). An extreme value model for predicting the results of horse races. Applied Statistics 33, 125–133.
Robinson, M. E., and Tawn, J. A. (1995). Statistics for exceptional athletics records. Applied Statistics 44, 499–511.
Scarf, P. A., and Laycock, P. J. (1996). Estimation of extremes in corrosion engineering. Journal of Applied Statistics 23, 621–643.
Smith, R. L. (1986). Extreme value theory based on the r largest annual events. Journal of Hydrology 86, 27–43.
Weissman, I. (1978). Estimation of parameters and quantiles based on the k largest observations. Journal of the American Statistical Association 73, 812–815.
Tawn, J. A. (1988b). An extreme value theory model for dependent observations. Journal of Hydrology 101, 227–250.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag London
About this chapter
Cite this chapter
Coles, S. (2001). Classical Extreme Value Theory and Models. In: An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics. Springer, London. https://doi.org/10.1007/978-1-4471-3675-0_3
Download citation
DOI: https://doi.org/10.1007/978-1-4471-3675-0_3
Publisher Name: Springer, London
Print ISBN: 978-1-84996-874-4
Online ISBN: 978-1-4471-3675-0
eBook Packages: Springer Book Archive