Re: Multinomial approximation to Poisson ??

Nag wrote:
Hi:

I am trying to approximate a Poisson (L) with a multinomial (k+1
states: 0,1,...,k) distribution, n trials; i.e. n(0) + n(1) + n(2) +
...+ n(k) = n.

Given L and n, how does one determine the probabilities of the (k+1)
states?

Any references, suggestions?

I don't quite know what you mean: a Poisson is a univariate distribution, whilst a multinomial is multivariate.

But, if it helps, if A_i~Po(L_i), for i=1,..,n, then the vector of A's follow a multinomial with sum(A_i) trials, and p_i=L_i/sum(L_i). Proofs of this are in books on categorical data analysis, or generalized linear models.

Bob

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Bob O'Hara
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