Poisson distribution test

[eq]

Does any one know the references (sites or literature) that concerns
diffrent tests
about wheter a sample comes from Poisson distribution ??

I performed KS test in SPSS several times on difrent random samples of
cases in total sample.
The probability of rejection is about 0,5 , so I need stronger test.

Tnx in advance.

[David Jones]

You say "I need stronger test" : to get the "best test" you need to think about what departures from the Poisson distribution your problem is most sensitive to. There are various possibilities (i) more (or fewer) zero values than a Poisson distribution would suggest; (ii) longer (or shorter) tails.

One test that is simple and easily interpretable is based on the coefficient of dispersion (ratio of variance to mean), but this may not have good power against alternatives you are interested in.

You may find the idea of testing against a negative binomial alternative useful. Or you could look for other families of discrete ditributions that have the Poisson as a special case.

There are even graphical-based approaches such as lookingh at the ratios of estimates Pr(N=n+1)/Pr(N=n), which should turn out to roughly constant with n, and for which particular patterns may suggest certain alternatives.

David Jones

[Russell]

You might try this. No guarantees it will solve
your problem.

Martin, R. L., "A Statistic Useful for Characterizing
Probability Distributions, with Application to Rain
Rate Data", J. Appl. Meteor., 28, 354 (1989)

Cheers,
Russell

[duncan smith]

If you keep trying different tests you will most likely eventually find
one that results in a 'significant' p-value, regardless of whether the
null hypothesis is true or false. Also, if you keep testing different
subsamples you'll probably eventually find a subsample that leads to
rejection. Can you see why doing this is wrong?

Duncan