Abstract
This chapter deals once again with the central topic of this book, namely with exceedances (in other words, peak-over-threshold values) over high thresholds and upper order statistics. One may argue that this chapter (in conjuction with the consecutive chapter) is richer and more exciting than the preceding one concerning maxima. The role of extreme value (EV) dfs is played by generalized Pareto (GP) dfs.
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References
Reiss, R.-D., Haßmann, S. and Thomas, M. (1994). XTREMES: Extreme value analysis and robustness. In [11], Vol. 1. 175–187.
Prescott, P. and Walden, A.T. (1980). Maximum likelihood estimation of the parameters of the generalized extreme—value distribution. Biometrika 67, 723–724.
Dekkers, A.L.M., Einmahl, J.H.J. and de Haan, L. (1989). A moment estimator for the index of an extreme—value distribution. Ann. Statist. 17, 1833–1855.
Pickands, J. (1975). Statistical inference using extreme order statistics. Ann. Statist. 3, 119–131.
Drees, H. (1995). Refined Pickands estimators of the extreme value index. Ann. Statist. 23, 2059–2080.
Haan, de L., Peng, L. and Vries, de C.G. (1996) Using a bootstrap method to choose the sample fraction in tail index estimation.
Drees, H. and Kaufmann, E. (1996). Selection of the optimal sample fraction in univariate extreme value estimation.
Csörgö, S., Deheuvels, P. and Mason, D.M. (1985). Kernel estimates of the tail index of a distribution. Ann. Statist. 13, 1050–1078.
Rasmussen, P.F., Ashkar, F., Rosbjerg, D. and Bobée, B. (1994). The pot method for flood estimation: a review, 15–26 (in [9]).
Langbein, W.B. (1949). Annual floods and the partial duration flood. Transactions Geophysical Union 30, 879–881.
Taken from the paper by Davison and Smith (page ix).
Hashofer, A.M. and Wang, Z. (1992). A test for extreme value domain of attraction. JASA 87, 171–177.
Weissman, I. (1978). Estimation of parameters and large quantiles based on the k largest observations. JASA 73, 812–815.
Benktander, G. (1970). Schadenverteilung nach Grösse in der Nicht-Leben-Versicherung. Mitteil. Schweiz. Verein Versicherungsmath., 263–283
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Reiss, RD., Thomas, M. (1997). Generalized Pareto Models. In: Statistical Analysis of Extreme Values. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6336-0_5
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DOI: https://doi.org/10.1007/978-3-0348-6336-0_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-5768-9
Online ISBN: 978-3-0348-6336-0
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