I can find Hypothesis test for poisson distribution on the internet as below example, but seems JMP does not have such test (I can't find cumulative tables for poisson distribution in JMP)? And another question is when the distribution is gamma poisson, how do i modify test method?
An existing car model is known to break down on average 1.5 times/ per year. Now we want to test if new designed model is less likely to break down with ten randomly selected cars break down a total of 8 times within the first year.
Let X be the number of break downs of the new model of car in a year. X∼Poisson(λ) with λ=1.5. The null and alternative hypotheses will be
H1: λ <1.5.
We need to decide whether P[X≤8]<α, where α=0.05. Firstly, the expected number of breakdowns λt =1.5×10=15. We use the cumulative tables with λt =15 and x=8 to see P[X≤8]=0.0374
P[X≤8] = 0.0374 < 0.05
so we accept the alternative hypothesis. The average rate of breakdowns has decreased.
I understand that there is no direct test of the gamma poisson population parameter. Here are two things, though, that might help you.
First, you can use the JSL probability functions (PDF, CDF, and inverse CDF) in a script editor or a column formula to create such a table. A quick way to find this information is to select Help > Scripting Index. Change the filter to Functions (top left button) and then select the Probability group. The second list will contain the distribution functions.
Second, you can ask for quantiles after you fit the gamma poisson distribution model. The command is in the red triangle menu for the fit.