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Functional Laws of Small Numbers

In: Laws of Small Numbers: Extremes and Rare Events

Author

Listed:
  • Michael Falk

    (University of Würzburg, Institute of Applied Mathematics and Statistics)

  • Rolf-Dieter Reiss

    (University of Siegen, Department of Mathematics)

  • Jürg Hüsler

    (University of Berne, Department of Mathematical Statistics and Actuarial Science)

Abstract

We will develop in the following a particular extension of the well known Poisson approximation of binomial distributions with a small hitting probability, which is known as the law of small numbers. This extension, which one might call functional laws of small numbers, links such seemingly different topics like nonparametric regression analysis and extreme value theory.

Suggested Citation

  • Michael Falk & Rolf-Dieter Reiss & Jürg Hüsler, 2004. "Functional Laws of Small Numbers," Springer Books, in: Laws of Small Numbers: Extremes and Rare Events, edition 0, chapter 0, pages 3-22, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-7791-6_1
    DOI: 10.1007/978-3-0348-7791-6_1
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