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Functional Laws of Small Numbers

In: Extreme Value Theory and Applications

Author

Listed:
  • Michael Falk

    (Katholische Universität Eichstätt, Geographische Fakultät)

  • Rolf-Dieter Reiss

    (Universität GH Siegen, Fachbereich Mathematik)

Abstract

This article describes a particular extension of the famous Poisson approximation of binomial distributions with small hitting probability, known as the law of small numbers. By this extension, which one might call functional law of small numbers, we can typically derive an approximation of the distribution of those random elements among independent replicates of a random element Z, which fall into a given subset A of the sample space having but a small probability P{Z ∈ A} of occurrence. If this subset A is located in the center of the distribution of Z, then regression analysis turns out to be within the scope of this extension. If A is located at the border, then extreme value theory is covered by this approach.

Suggested Citation

  • Michael Falk & Rolf-Dieter Reiss, 1994. "Functional Laws of Small Numbers," Springer Books, in: Janos Galambos & James Lechner & Emil Simiu (ed.), Extreme Value Theory and Applications, pages 337-354, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-3638-9_20
    DOI: 10.1007/978-1-4613-3638-9_20
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