论文标题
评估皮特曼分区长度的时刻
Evaluating moments of length of Pitman partition
论文作者
论文摘要
Pitman采样公式已被深入研究，作为随机分区的分布。感兴趣的对象之一是$ k（= k_ {n，θ，α}）$的随机分区，该分区遵循Pitman采样公式，其中$ n \ in \ Mathbb {n} $，$α\ in（0，\ infty）$ and $θ>-α$是参数。本文介绍了其$ r $ $ $ \ mathsf {e} [k^r] $（$ r = 1,2，\ ldots $）的渐近评估。特别是，这项研究的目标是提供比以前开发的$ \ Mathsf {e} [k^r] $作为$ n \ to \ infty $更近似的评估，并提供了$ \ mathsf {e} [e} [e} [k^r] $的近似评估，作为参数$ n $ n $ n $ n $ n $ n $ n $ n $ s $ nift $ untine $ nift $ untine $ nity untient $ nity ni可能/$ nige to $/ni可能/$ nity ni可能/$/yins $/ni可能。本文提出的结果将为$ k $的渐近行为提供更准确的理解。
The Pitman sampling formula has been intensively studied as a distribution of random partitions. One of the objects of interest is the length $K (= K_{n,θ,α})$ of a random partition that follows the Pitman sampling formula, where $n\in\mathbb{N}$, $α\in(0,\infty)$ and $θ> -α$ are parameters. This paper presents asymptotic evaluations of its $r$-th moment $\mathsf{E}[K^r]$ ($r=1,2,\ldots$) under two asymptotic regimes. In particular, the goals of this study are to provide a finer approximate evaluation of $\mathsf{E}[K^r]$ as $n\to\infty$ than has previously been developed and to provide an approximate evaluation of $\mathsf{E}[K^r]$ as the parameters $n$ and $θ$ simultaneously tend to infinity with $θ/n \to 0$. The results presented in this paper will provide a more accurate understanding of the asymptotic behavior of $K$.
