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1 results

  • A Pólya Approximation to the Poisson-Binomial Law

  • Part of
  • Max Skipper
  • Journal:
    Journal of Applied Probability / Volume 49 / Issue 3 / September 2012
    Published online by Cambridge University Press:
    04 February 2016, pp. 745-757
    Print publication:
    September 2012
    • Article
      • You have access
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  • Using Stein's method, we derive explicit upper bounds on the total variation distance between a Poisson-binomial law (the distribution of a sum of independent but not necessarily identically distributed Bernoulli random variables) and a Pólya distribution with the same support, mean, and variance; a nonuniform bound on the pointwise distance between the probability mass functions is also given. A numerical comparison of alternative distributional approximations on a somewhat representative collection of case studies is also exhibited. The evidence proves that no single one is uniformly most accurate, though it suggests that the Pólya approximation might be preferred in several parameter domains encountered in practice.