Abstract
A step is described toward better statistical treatment of data for tail estimation. The classical extreme value theory together with its practical inefficiency for tail inference are discussed briefly. The threshold method that utilizes available information in a more efficient manner is described, and its relation to extreme value theory is mentioned. Some comparison is also made using two sets of published data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bardslley, W. E., 1988, Toward a General Procedure for Analysis of Extreme Random Events in the Earth Sciences: Math. Geol., v. 20, n. 5, p. 513–528.
Benjamin, J. R., and Cornell, C. A., 1970, Probability, Statistics and Decision for Civil Engineers, McGraw-Hill, New York, 684 p.
Cook, N. J., 1982, Towards Better Estimation of Extreme Winds: J. Wind Eng. Ind. Aerodyn., v. 9, p. 295–323.
Cox, D. R., and Lewis, P. A. W., 1966, The Statistical Analysis of Series of Events, Chapman and Hall, London, 285 p.
David, H. A., 1981, Order Statistics, John Wiley, New York, 360 p.
Davison, A., 1984, Modelling Excesses over High Thresholds, With an Application. In Statistical Extremes and Applications, in J. Tiago de Oliveira (Ed.), D. Reidel, Dordrecht, p. 461–482.
Dekkers, A. L. M., and De Haan, L., 1987, On a Consistent Estimate of the Index of an Extreme Value Distribution, Report MS-R8710, Center for Math. and Comp. Science, Amsterdam, The Netherlands, 17 p.
Dorman, C. M. L., 1982, Extreme Values: An Improved Method of Fitting: J. Wind Eng. Ind. Aerodyn., v. 10, p. 177–190.
DuMouchel, W., 1983, Estimating the Stable Index α in Order to Measure Tail Thickness: Ann. Statist., v. 11, p. 1019–1036.
Fisher, R. A., and Tippett, L. H. C., 1928, Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample: Proc. Cambridge Philos. Soc., v. 24, p. 180–190.
Galambos, J., 1987, The Asymptotic Theory of Extreme Order Statistics: Wiley, New York, 2nd ed., 352 p.
Gumbel, E. J., 1958, Statistics of Extremes, Columbia University Press, New York, 375 p.
Hall, P., 1982, On Estimating the Endpoint of a Distribution: Ann. Statist., v. 10, p. 556–568.
Hill, B. M., 1975, A Simple General Approach to Inference about the Tail of a Distribution: Ann. Statist., v. 3, p. 1163–1174.
Hinkley, D. V., 1969, On the Ratio of Two Correlated Normal Variables: Biometrika, v. 56, p. 635–640.
Hogg, R. V., and Tanis, E. A., 1983, Probability and Statistical Inference, 2nd ed. Macmillan, New York, 533 p.
Johnson, N. L., and Kotz, S., 1972, Distributions in Statistics (Continuous Multivariate Distributions). John Wiley & Sons, New York, 322 p.
Leadbetter, M. R., Lindgren, G., and Rootzen, H., 1983, Extremes and Related Properties of Random Sequences and Series, Springer-Verlag, New York, 336 p.
NERC, The Flood Studies Report, 1975, National Environment Research Council, London, v. 1–5, Bibliography, v. 1, p. 483–485.
North, M., 1980, Time-Dependent Stochastic Models of Floods: J. Hyd. Div. ASCE, v. 106, p. 649–655.
Pericchi, L. R., and Rodrigues-Iturbe, I., 1985, On Statistical Analysis of Floods, in A. C. Atkinson and S. E. Fienberg (eds.) A Celebration of Statistics, The ISI Centenary Volume, Springer-Verlag, New York, p. 521–523.
Pickands, J., 1975, Statistical Inference Using Extreme Order Statistics: Ann. Statist., v. 3, p. 119–131.
Pourahmadi, M., 1989, Estimation and Interpolation of Missing Values of a Stationary Time Series: J. Time Series Analysis: v. 10, p. 1–21.
Prescott, P., and Walden, A. T., 1983, Maximum likelihood estimation of the Three-Parameter Generalized Extreme-Value Distribution from Censored Samples: J. Statist. Comput. Simul., v. 16, p. 241.
Rijkoort, P. J., and Wierings, J., 1983, Extreme Wind Speeds by Compound Weibull Analysis of Exposure-Corrected Data: J. Wind. Eng. Ind. Aerodyn., v. 13, p. 93–104.
Schuster, E. F., 1984, Classification of Probability Laws by Tail Behavior: J. Amer. Stat. Assoc., v. 79, p. 936–939.
Smith, R. L., 1987, Estimating Tails of Probability Distributions: Ann. Statist., v. 15, p. 1174–1207.
Todorovic, P., 1979, A Probabilistic Approach to Analysis and Prediction of Floods: Proc. of the 42nd Section of the ISI, International Statistical Institute, Buenos Aires, p. 113–124.
Von Mises, R., 1936, La Distribution de la plus Grande n Valeurs, in Selected Papers II, American Mathematical Society, Providence, p. 271–294.
Weibull, W., 1939, A Statistical Theory of Strength of Material, Ingeniors Vetenskaps Akademien handlingar, n. 151, 139 p.