Harremoës, P and Johnson, O and Kontoyiannis, I (2007) *Thinning and the law of small numbers.* In: UNSPECIFIED pp. 1491-1495..

## 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. ©2007 IEEE.

Item Type: | Conference or Workshop Item (UNSPECIFIED) |
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Subjects: | UNSPECIFIED |

Divisions: | Div F > Signal Processing and Communications |

Depositing User: | Cron Job |

Date Deposited: | 08 Jan 2018 20:12 |

Last Modified: | 15 Oct 2020 03:45 |

DOI: | 10.1109/ISIT.2007.4557433 |