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On the Poisson-binomial relative error

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  • Antonelli, Sabrina
  • Regoli, Giuliana

Abstract

This paper analyses the goodness of Poisson approximation to the binomial distribution with parameters n and p. In order to stress the importance of the smallness of p to obtain a good approximation, the relative error is analysed when p is fixed and n tends to infinity. We find the relative error pointwise limit and its asymptotic distribution; we also show that the asymptotic mean relative error gives an approximation of the mean relative error. Finally we give numerical estimates of all these approximations.

Suggested Citation

  • Antonelli, Sabrina & Regoli, Giuliana, 2005. "On the Poisson-binomial relative error," Statistics & Probability Letters, Elsevier, vol. 71(3), pages 249-256, March.
  • Handle: RePEc:eee:stapro:v:71:y:2005:i:3:p:249-256
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    Cited by:

    1. Antonelli, Sabrina & Regoli, Giuliana, 2009. "Asymptotic distribution of density ratios," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 289-294, February.

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