Finitizing power series distributions

Finitization converts a discrete power series distribution into another distribution with smaller support of specified finite size. A useful and remarkable property of our finitization method is that when applied to the Poisson distribution, it preserves the moments of the original Poisson distribution up to the order of finitization under a parameter restriction. Finitization also has interesting and practical probability modeling applications, especially in fast random variate generation via the method of aliasing.