Factorial Moment Characterizations for Certain Binomial-Type Distributions
Adrienne W. Kemp, C. D. Kemp · Communication in Statistics- Theory and Methods · 2004
This article obtains characterizations for the binomial, Grassia I-binomial, (carrier-borne epidemic), and randomized occupancy distributions via their factorial moments. The characterizing condition has the form: where μ[r]′ denotes the rth factorial moment, a and b are parameters, and θ(a, b, r) is the ratio of two functions linear in r. Given support 0, 1,…, n, then the ratio μ[r]′/μ2 is an ancillary statistic that is equal, greater than, or less than (n − 1)/n for the three distributions, respectively. The use of the ancillary statistic is demonstrated.