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.
Similar content being viewed by others
References
Canfield, E. (1977). Central and Local Limit Theorems for the Coefficients of Polynomials of Binomial Type,J. Combinatorial Theory Ser. A,23, 275–290.
Cacoullos, T. and Charalambides, Ch. (1975). On minimum variance unbiased estimation for truncated binomial and negative binomial distributions,Ann. Inst. Statist. Math.,27-2, 235–244.
Charalambides, Ch. (1977). A new kind of numbers appearing in then-fold convolution of truncated binomial and negative binomial distributions,SIAM J. APPL. MATH.,33-2), 279–288.
Comtet, L. (1972). ANALYSE COMBINATOIRE, Nombres de Stirling généraux et fonctions symetriques.C. R. Acad. Sc. Paris, t. 275, Série A, 747–750.
Patil, G. P. (1963). Minimum variance unbiased estimation and certain problems of additive number theory,Ann. Math. Stat.,34, 1050–1056.
Author information
Authors and Affiliations
About this article
Cite this article
Kyriakoussis, A. Asymptotically minimum variance unbiased estimation for a class of power series distributions. Ann Inst Stat Math 37, 241–250 (1985). https://doi.org/10.1007/BF02481095
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02481095