"In one of the first studies of the Poisson distribution, von Bortkiewicz considered the frequency of deaths from kicks in the Prussian army corps. From the study of 14 corps over a 20-year period, he obtained the data shown in [the] Table. Fit a Poisson distribution to this data and see if you think that the Poisson distribution is appropriate."
We can think of the results for each corps over a single year as a Bernoulli trial with n very large and p very small and the mean near 1. We calculate the mean as (91 + 2*32 + 3*11 + 4*2) / 280 = 0.7. So λ = 0.7.
The code below prints the values for P(0), P(1) etc, as well as the calculated probability given this λ, and the expected and observed values for the number of corps with x deaths. The output is:
I think the model fits the data pretty well. However, I would like to know the appropriate statistical test for the fit.