On arbitrarily underdispersed discrete distributions

Abstract:

We review a range of generalized count distributions, investigating which (if any) can be arbitrarily underdispersed, i.e., its variance can be arbitrarily small compared to its mean. A philosophical implication is that models failing this criterion perhaps should not be considered a “statistical model” according to the extendibility criterion of McCullagh (2002). Four practical implications will be discussed. We suggest that all generalizations of the Poisson distribution be tested against this property.

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