The Stirling Turn

Stirling Distributions and Stirling

The left-truncated generalized Poisson distribution belongs to the family of the modified power series distributions. Using sufficiency and completeness of £ ^ x . (minx , , $ 3 x 0 ) respectively, when the truncation point is known (resp. unknown), the minimum variance unbiased (M.V.U) estimator for certain functions of the parameter $ (resp. 0, r) involved in these distributions can be obtain...

The p-Stirling Numbers

The purpose of this article is to introduce p-Stirling numbers of the first and second kinds.

To the Framingham data, turn, turn, turn.

The r-Stirling numbers

The r-Stifling numbers of the first and second kind count restricted permutations and respectively restricted partitions, the restriction being that the first r elements must be in distinct cycles and respectively distinct subsets. The combinatorial and algebraic properties of these numbers, which in most cases generalize similar properties of the regular Stirling numbers, are explored starting...

The D-Stirling Numbers

Abstract In this paper, we introduce a kind of combinatorial numbers, D − Stirling numbers, and its special cases. An exponential generating function of the D − Stirling numbers is given. We also present recurrence relations, monotonicity, and limiting properties of the D−Stirling numbers. Applications to statistical probability function estimation and restricted occupancy theory are provided. ...