In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments as do (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a new identity for 'moments' of partitions of numbers. The general limiting result is then used to (re-)derive asymptotic normality for several models including classical discrete distributions, occupancy problems in some generalized allocation schemes and two models related to negative multinomial distribution.

中文翻译：

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通过因子累积量和划分身份的渐近正态性。

在论文中，我们通过阶乘累积量开发了一种渐近正态性的方法。阶乘累积量从阶乘矩中产生的方式与（普通）累积量从（普通）矩中产生的方式相同。我们利用的另一个工具是数字分区“时刻”的新身份。然后使用一般限制结果（重新）推导几种模型的渐近正态性，包括经典离散分布、一些广义分配方案中的占用问题以及与负多项式分布相关的两个模型。