退化二项和退化Poisson随机变量
Degenerate binomial and degenerate Poisson random variables
摘要：
本文的目的是研究Poisson随机变量与Lah-Bell多项式的关系以及退化二项式和退化Poisson随机变量与退化Lah-Bell多项式的关系。除此之外，我们还证明了带参数α的退化Poisson随机变量的上升阶乘矩由退化Lah-Bell多项式在α处的值给出.我们还证明了退化Poisson随机变量的概率母函数等于退化Lah-Bell多项式的母函数。此外，我们显示了类似的结果，泊松随机变量。这里的第n个Lah-Bell数计算一组n个元素可以被划分成非空线性有序子集的方式的数量，Lah-Bell多项式是Lah-Bell数的自然扩张，退化Lah-Bell多项式是Lah-Bell多项式的退化版本。
英文摘要：
The aim of this paper is to study the Poisson random variables in relation to the Lah-Bell polynomials and the degenerate binomial and degenerate Poisson random variables in connection with the degenerate Lah-Bell polynomials. Among other things, we show that the rising factorial moments of the degenerate Poisson random variable with parameter α are given by the degenerate Lah-Bell polynomials evaluated at α. We also show that the probability-generating function of the degenerate Poisson random variable is equal to the generating function of the degenerate Lah-Bell polynomials. Also, we show similar results for the Poisson random variables. Here the nth Lah-Bell number counts the number of ways a set of n elements can be partitioned into non-empty linearly ordered subsets, the Lah-Bell polynomials are natural extensions of the Lah-Bell numbers and the degenerate Lah-Bell polynomials are degenerate versions of the Lah-Bell polynomials.
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