Abstract
Chapter 1 is basic for the understanding of the main subjects treated in this book. It is assumed that the given data are generated according to a random mechanism that can be linked to some parametric statistical model.
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References
Seal, H.L. (1969). Stochastic Theory of a Risk Business. Wiley, New York.
BĂĽuhlmann, H. (1970). Mathematical Methods in Risk Theory. Springer, Berlin.
Kolata, G. New views on life spans alter forecasts on elderly. The New York Times, Nov. 16. 1992.
We refer to Haight, F.A. (1967). Handbook of the Poisson Distribution. Wiley, New York; for a more recent monograph see Barbour, A.D., Holst, L. and Janson, S. (1992). Poisson Approximation. Oxford Studies in Probability. Oxford University Press.
Mises von, R. (1936). La distribution de la plus grande de n valeurs. Rev. Math. Union Interbalcanique 1, 141–160. Reproduced in Selected Papers of Richard von Mises, Amer. Math. Soc. 2 (1964), 271–294.
Jenkinson, A.F. (1955). The frequency distribution of annual maximum (or minimum) values of meteorological elements. Quart. J. Roy. Meteorol. Soc. 81, 158–171.
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. Camb. Phil. Soc. 24, 180–190.
Balkema, A.A. and de Haan, L. (1974). Residual life time at great age. Ann. Probab. 2, 792–804. Parallel work was done by J. Pickands (1975). Statistical inference using extreme value order statistics. Ann. Statist. 3, 119–131.
Drees, H. and Reiss, R.-D. (1992). Tail behavior in Wicksell’s corpuscle problem. In: Probability Theory and Applications, J. Galambos and I. Kátai (eds.), 205–220, Kluwer, Dortrecht.
Reiss, R.-D. (1989). Robust statistics: A converse view. 23rd Semester on Robustness and Nonparametric Statistics. Stefan Banach Center, Warsaw, Abstracts of Lectures, Part II, 183–184.
For details see, e.g., Devroye, L. (1986). Non-Uniform Random Variate Generation. Springer, New York.
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(2007). Parametric Modeling. In: Statistical Analysis of Extreme Values. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7399-3_1
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DOI: https://doi.org/10.1007/978-3-7643-7399-3_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7230-9
Online ISBN: 978-3-7643-7399-3
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