Multiparameter Stirling and C-Type Distributions
The distribution of the sufficient statistic for a one-parameter power series distribution (PSD) truncated on the left at several known or unknown points is derived. The special cases of the logarithmic series, the Poisson, and the binomial and negative binomial distributions lead to multiparameter first- and second-type Stirling distributions and C-type distributions, respectively. Certain new kinds of numbers are defined in terms of partial finite differences of corresponding multiparameter Stirling and C-numbers. Minimum variance unbiased estimators are provided for the parametric function θα (α positive integer, θ the parameter of the PSD) also in the case of unknown truncation points, and for the probability function only when the truncation points are known.
Key WordsPower series distributions multiple truncation minimum variance unbiased estimation multiparameter Stirling and C-numbers
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- Cacoullos, T. (1973b). Multiparameter Stirling and C- numbers. Submitted to SIAM J. Appl. Math.Google Scholar
- Cacoullos, T. (1973c). Minimum variance unbiased estimation for multiply truncated power series distributions. Submitted to SIAM J. Appl. Math.Google Scholar
- Cacoullos, T. and Charalambides, Ch. (1972). On minimum variance unbiased estimation for truncated binomial and negative binomial distributions. To appear in Ann. Inst. Statist. Math., Tokyo.Google Scholar
- Cacoullos, T. and Charalambides, Ch. (1972). Minimum variance unbiased estimation for truncated discrete distributions. Colloquia Mathematica Societatis Janos Bolyai, 9 European Meeting of Statisticians, Budapest.Google Scholar
- Charalambides, Ch. (1972). Minimum variance unbaised estimation for a class of left-truncated discrete distributions. Doctoral Thesis, Athens University, Athens, Greece. (In Greek)Google Scholar
- Charalambides, Ch. (1973a). The generalized Stirling and C-numbers. Sankhya Ser A (to appear).Google Scholar
- Charalambides, Ch. (1973b). Minimum variance unbaised estimation for a class of left-truncated discrete distributions. Sankhya Ser A (to appear).Google Scholar
- Joshi, S. W. (1972). Minimum variance unbiased estimation for truncated distributions with unknown truncation points. Tech. Rep., University of Austin, Texas.Google Scholar
- Joshi, S. W. (1975). In Statistical Distributions in Scientific Work, Volume I, Models and Structures, Patil, Kotz, and Ord (eds.). D. Reidel, Dordrecht and Boston, pp. 9 – 17.Google Scholar