Poisson Approximation

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


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.


Somatic Cell Hybrid White Ball Bernoulli Random Variable Poisson Approximation Total Variation Distance 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Kenneth Lange
    • 1
  1. 1.Department of Biostatistics and MathematicsUniversity of MichiganAnn ArborUSA

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