Estimation of the Parameters of the Triple and Quadruple Stuttering-Poisson Distributions

In this article we introduce multiple stuttering-Poisson distributions and discuss their genesis, properties and applications. We consider a special case of triple stuttering-Poisson distribution with probability generating function G(t) = Exp [a(t − 1) + b(t 2 − 1) + c(t 3 − l)] and investigate (1) maximum likelihood estimation, (2) moment estimation, and (3) mixed moment estimation of the parameters a, b, c. First order terms in the expressions for the biases and covariances of moment estimators are presented. The joint asymptotic efficiencies of moment estimators are tabulated for a few selected parameter points. The first order terms in the biases of maximum likelihood estimators and moment estimators are also given for a few selected parameter points. As judged from the contribution of the first order term, the possible bias of maximum likelihood estimators can be substantial over a considerable region of the parameter space. The moment estimators have low joint asymptotic efficiency over a large par...