Re: Multinomial approximation to Poisson ??


David Winsemius wrote:
"Reef Fish" <Large_Nassau_Gr0uper@xxxxxxxxx> wrote in
news:1157053711.591415.87030@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:


Nag wrote:

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?

Several!

The first is my 1992 paper in the American Statistician, "Just Say NO
to the use of Tables for the Binomial and Other Discrete
Distributions", pointing to two other reference that has the relation
of the Poisson to the Chi-Square distribution. >
There is NO NEED for any appromation to ANY Poisson probability! (Given
the widely available statistical packages that can calbulate the cdf of
the
chi-square distribution.

This is the excerpt from a recent post of mine:

The 1992 paper only high-lighted
the Binomial-F relation and pointed to the earlier
results I extracted out of Pratt's 1968 paper into one
little section in my 1978 approximation paper in JASA.

exact results can be quickly computed, but the
mathematical identities (5.1) - (5.6) in that paper
are the ones that
make some discrete distribution tables obsolete.

the relation between the Poisson tail and Chi-square
tail should be useful.

Note especially the last comment above.

Lecture time?

I was speaking of the approximation of Poisson PROBABILITIES.

It wasn't clear what Nag was asking, but based on what he explained
to Bob O'Hara:

Nag> Think of convergence of Binomial to Poisson. Binomial is
2-variate by
Nag> your argument and yet converges to a univariate Poisson. Given
Nag> Poisson(L) and n, Binomial(p,L/n) converges to Poisson (L) as n
-> oo.

It appears that Nag was talking about approximating the Poisson
PROBABILITIES still.

NOTHING about Poisson Regression or GLM or the rest of your comments.

One of us is singing in the wrong choir.

It could be me, but I don't think so.

-- Reef Fish Bob.


Log-linear models are often used to summarize and draw
inferences regarding multinomial problems. Poisson regression is a subset
of those methods. The GLM formulation supports inferences by comparing
deviances from nested models to chi-square ctritical values. I am
surmising that you might do the group a service by tying some of those
concepts together with a discussion of the relations between those
distributions.

--
David Winsemius.

.

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