Poisson Approximation

• Kenneth Lange
Part of the Statistics for Biology and Health book series (SBH)

Abstract

In the past few years, mathematicians have developed a powerful technique known as the Chen-Stein method [2, 4] for approximating the distribution of a sum of weakly dependent Bernoulli random variables. In contrast to many asymptotic methods, this approximation carries with it explicit error bounds. Let X α be a Bernoulli random variable with success probability p α where a ranges over some finite index set I. It is natural to speculate that the sum S = Σα∈1 X α is approximately Poisson with mean λ = Σα∈I p α. The Chen-Stein method estimates the error in this approximation using the total variation distance between two integer-valued random variables Y and Z.

Keywords

Somatic Cell Hybrid White Ball Bernoulli Random Variable Poisson Approximation Total Variation Distance
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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