Asymptotically minimum variance unbiased estimation for a class of power series distributions

Summary The problem of finding an asymptotically minimum variance unbiased estimator (A.M.V.U.E.) for the parameter of certain truncated power series distributions, is discussed, when the generating function of their coefficients are i) polynomials of binomial type ii) generalized ascending factorials iii) polynomials with coefficients the well known Eulerian numbers.