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Poisson approximation to the normal

  1. Sep 21, 2010 #1
    So my book merely mentions that this holds as a result of the central limit theorem for values of lambda greater than 10, but ideally greater than 32.

    Anyway I was wondering if anyone knew this actual proof as I am interested in seeing it step by step and I could not have found it anywhere that I have looked.

    Thanks
     
  2. jcsd
  3. Sep 22, 2010 #2

    mathman

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    I can't give you an off hand answer, but it is essentially based on the central limit theorem. Similar result holds for binomial distribution.
     
    Last edited: Sep 22, 2010
  4. Sep 22, 2010 #3
    The Berry-Esseen theorem is similar to CLT but gives a bound on the difference between the CDF of a sample mean and the normal CDF, in terms of n and the third moment.

    To use this theorem here, for example, write a high-frequency Poisson as a sum of low-frequency iid Poissons (e.g. [tex]\lambda=n.f[/tex] where f is a value between 0.9 and 1) and then find the value of n that gives the required accuracy.
     
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