"Daniel Hoppe" <[EMAIL PROTECTED]> wrote in message news:<asfb66$9b1$[EMAIL PROTECTED]>... > Dear all, > > I've a question regarding a goodness-of-fit to a Poisson distribution. I > have the following observations from a buying process which I expect to be > Poisson.distributed: > > 0 1 2 > 182 15 3 > > The mean and my estimator for lambda in the poisson distribution therefore > is 0.105 with the following expected frequencies: > 0 1 >1 > 180.0649 18.90681 1.028281 > > Now I would like to run a chi-squared goodness-of-fit test. But for this > test the expected frequencies should be >= 5, so I would need to join
That arbitrary rule of thumb is generally much too strict. You should be able to do reasonably well with the expectations you have. > classes "1" and ">1". If I have two classes and one estimated parameter, the > degrees of freedom should be 2 - 1 - 1 = 0 for the test which leads me to > the assumption that this is not a good idea and that I'm missing something. Important: To lose a full d.f., your degrees of freedom, calculations for the chi-squared test have to be based on the parameter estimates coming from the categories you use in the test. If you combine classes you have to use the combined data to estimate the parameter to lose a full d.f. If you use the original data to estimate the parameter but combine categories for the test, you lose less than a full d.f. > Could someone kindly give me a hint, how I could test for a > poisson-distribution in this case? First up, you should be okay just using the test as it stands. The p-values won't be exact, but they'll probably be reasonably close. The test suggested by Jim Snow is a good suggestion. Do you have some likely alternatives in mind? It might help! Glen . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
