A class of discrete distributions suited to fitting very long-tailed data

This paper proposes a mixed Poisson distribution which has a very long tail and also examines the full beta model of Kempton (Biometrika, 1975). The proposed distribution has a three-term probability recurrence relation that is stable in the backward direction, which is computationally desirable.The flexibility of the distribution to fit very long-tailed data is examined. The computation of probabilities is discussed and a numerical example is given.