Re: Multinomial approximation to Poisson ??

Nag wrote:
Hi guys:

Thanks for the responses. Let me clarify my query.

1. I need to find a k-nomial distribution X such that

X = X1 + X2 + .... + Xn

where each Xi has k+1 outcomes: 0, 1, ..., k and the Xi's are iid.

How do I determine the probabilities such that X converges to a
Poisson (L) distribution as n increases to infinity.

So is X the sum of n binomial distribtions? If so, you need the probabilities to be equal, in whch case this just boils down to a binomial.

If they're not equal, then X has a mixture distribution, so there will be excess variation over the binomial and hence excess over any Poisson approximation.

Bob

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Bob O'Hara

Dept. of Mathematics and Statistics
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