In this chapter, we catch a glimpse of the real world in the condensed form of data. Our primary aim is to fit extreme value (EV) and generalized Pareto (GP) distributions, which were introduced in the foregoing chapter by means of limit theorems, to the data.


Hazard Function Kernel Density Tail Dependence Excess Function Cluster Size Distribution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Marron, J.S. (1988). Automatic smoothing parameter selection: A survey. Empirical Economics 13, 187–208.CrossRefGoogle Scholar
  2. 2.
    who discussed the problem of outliers: “... the rejection of observations is too crude to be defended: and unless there are other reasons for rejection than the mere divergences from the majority, it would be more philosophical to accept these extremes, not as gross errors, but as indications that the distribution of errors is not normal” on page 322, respectively, page 289 in Fisher, R.A. (1922). On the mathematical foundation of theoretical statistics. Phil. Trans. Roy. Soc. A 222, 309–368, and Collected Papers of R.A. Fisher, Vol. I, J.H. Bennett, ed., pp. 274–335. University of Adelaide, 1971.CrossRefGoogle Scholar
  3. 3.
    Drees, H. and Reiss, R.-D. (1996). Residual life functionals at great age. Commun. Statist.-Theory Meth. 25, 823–835.MATHCrossRefGoogle Scholar
  4. 4.
    Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality etc. Phil. Trans. Roy. Soc. 115, 513–585.CrossRefGoogle Scholar
  5. 5.
    Pruscha, H. (1989). Angewandte Methoden der Mathematischen Statistik. Teubner, Stuttgart.MATHGoogle Scholar
  6. 6.
    Sibuya, M. (1960). Bivariate extreme statistics. Ann. Inst. Math. Statist. 11, 195–210.MATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag AG 2007

Personalised recommendations