In the following question, I'd like to know if this approach is plausible? By the method of moments (lambda) is equal to 3.846. To find the expected number of weeks, for example, for zero claims per week, (e^(-(lambda)))*52, which gives, 1.1108, similarly expected number of weeks for one claim (lambda)*(e^(-(lambda)))*52, which gives, 4.2723 and likewise and then perform a chi squared goodness of fit test with 8 degrees of freedom. If not, what is the correct approach, and the second part of the question asks about serial correlations test, how can one go about the second part?
Yes 1st part to fit Poisson process is correct. The company might perform serial correlation test on the experience in order to check the problem of the inability of the chi square test to detect excessive clumping of no of claims over a given week.
