Functional Laws of Small Numbers

Michael Falk (), Jürg Hüsler () and Rolf-Dieter Reiss ()
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Michael Falk: University of Würzburg, Institute of Mathematics
Jürg Hüsler: University of Berne, Department of Mathematical Statistics and Actuarial Science
Rolf-Dieter Reiss: University of Siegen, Department of Mathematics

Chapter Chapter 1 in Laws of Small Numbers: Extremes and Rare Events, 2011, pp 3-23 from Springer

Abstract: 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 non-parametric regression analysis and extreme value theory.

Keywords: Variational Distance; Random Element; Empirical Process; Generalize Pareto Distribution; Data Versus (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0009-9_1

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DOI: 10.1007/978-3-0348-0009-9_1

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