A review of the Stirling numbers, their generalizations and statistical applications. (English) Zbl 0696.62025

Charalambides, Ch. A.; Singh, Jagbir

Commun. Stat., Theory Methods 17, No. 8, 2533-2595 (1988).

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:

62E10	Characterization and structure theory of statistical distributions
65C30	Numerical solutions to stochastic differential and integral equations

Keywords:

truncated distributions; generalized (compound) distributions; Stirling numbers; occupancy distributions