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A review of the Stirling numbers, their generalizations and statistical applications. (English) Zbl 0696.62025
Summary: The basic properties of the Stirling numbers and their generalizations are reviewed. Statistical applications of these numbers in expressing (i) the distribution of successes in Poisson (generalized Bernoulli) trials, (ii) the occupancy distributions, (iii) the convolutions of truncated power series distributions and related minimum variance unbiased estimators and (iv) the generalized discrete distributions and factorial moments are presented.
MSC:
62E10Characterization and structure theory of statistical distributions
65C30Stochastic differential and integral equations