Functional Laws of Small Numbers

Michael Falk () and Rolf-Dieter Reiss ()
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Michael Falk: Katholische Universität Eichstätt, Geographische Fakultät
Rolf-Dieter Reiss: Universität GH Siegen, Fachbereich Mathematik

A chapter in Extreme Value Theory and Applications, 1994, pp 337-354 from Springer

Abstract: 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.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-3638-9_20

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DOI: 10.1007/978-1-4613-3638-9_20

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