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I am using a Gaussian distribution to generate a Poisson variable with parameter $\lambda$. According to Wikipedia, when $\lambda > 1000$ this approximation is pretty good. However, using MATLAB I noticed that even when $\lambda = 400$ Gaussian and Poisson distributions seem to be almost identical.
What do you think would be the minimum value of $\lambda$ to guarantee that the two distributions are close enough?

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"What do you think would be the minimum value of $\lambda$ to guarantee that the two distributions are close enough?" - most likely it depends on the computing environment... –  J. M. May 11 '11 at 18:53
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And it also depends on what "close enough" means to you. –  Mike Spivey May 11 '11 at 19:06
    
I do not have any specific definition of closeness per se, but the value given on wikipedia has no justification either. I am simply looking for something that makes sense. –  ACAC May 11 '11 at 19:44

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up vote 4 down vote accepted

See this, in particular the section "General bound on error".

The article was written by user John D. Cook.

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