# Poisson approximation to the normal

1. Sep 21, 2010

### rhyno89

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. Sep 22, 2010

### mathman

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
3. Sep 22, 2010

### bpet

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. $$\lambda=n.f$$ 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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