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Thinning and the Law of Small Numbers | IEEE Conference Publication | IEEE Xplore

Thinning and the Law of Small Numbers


Abstract:

The "thinning" operation on a discrete random variable is the natural discrete analog of scaling a continuous variable, i.e., multiplying it by a constant. We examine the...Show More

Abstract:

The "thinning" operation on a discrete random variable is the natural discrete analog of scaling a continuous variable, i.e., multiplying it by a constant. We examine the role and properties of thinning in the context of information-theoretic inequalities for Poisson approximation. The classical Binomial-to-Poisson convergence, often referred to as the "law of small numbers," is seen to be a special case of a thinning limit theorem for convolutions of discrete distributions. A rate of convergence is also provided for this limit. A Nash equilibrium is established for a channel game, where Poisson noise and a Poisson input are optimal strategies. Our development partly parallels the development of Gaussian inequalities leading to the information- theoretic version of the central limit theorem.
Date of Conference: 24-29 June 2007
Date Added to IEEE Xplore: 09 July 2008
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Conference Location: Nice, France

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