I am aware of extreme value theory for continuous distributions. I need to fit an extreme value distribution to the maximum observation of number of events on a day, per month. This seems to be the block maxima problem, which is approximated by the GEV family of distributions for continuous distributions. How do I do this for count data?
As a secondary question, let's assume the basic count process is ~ Poisson. Then does this lead to a different answer to the original question?