Summary
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.
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© 1975 D. Reidel Publishing Company, Dordrecht-Holland
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Cacoullos, T. (1975). Multiparameter Stirling and C-Type Distributions. In: Patil, G.P., Kotz, S., Ord, J.K. (eds) A Modern Course on Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1842-5_3
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DOI: https://doi.org/10.1007/978-94-010-1842-5_3
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