Thinning and the Law of Small Numbers

@article{Harremos2007ThinningAT,
  title={Thinning and the Law of Small Numbers},
  author={Peter Harremo{\"e}s and Oliver Johnson and Ioannis Kontoyiannis},
  journal={2007 IEEE International Symposium on Information Theory},
  year={2007},
  pages={1491-1495}
}
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… CONTINUE READING
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