Central Limit Theorems for Additive Tree Parameters with Small Toll Functions
Central Limit Theorems for Additive Tree Parameters with Small Toll Functions
复制标题
具有小收费函数的可加树参数的中心极限定理
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
S. Wagner
中科院分区：
文献类型：
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作者：
S. Wagner
如果树参数可以递归地确定为所有分支的参数值之和加上某个收费函数，则我们将其称为树参数加法。在本文中，我们证明了非常一般的收费函数的中心极限定理，前提是它们有界且平均较小。考虑简单生成的树族以及 Pólya 树、递归树和二叉搜索树，结果通过我们证明正态或对数正态极限定律的几个参数示例来说明。
We call a tree parameter additive if it can be determined recursively as the sum of the parameter values of all branches, plus a certain toll function. In this paper, we prove central limit theorems for very general toll functions, provided that they are bounded and small on average. Simply generated families of trees are considered as well as Pólya trees, recursive trees and binary search trees, and the results are illustrated by several examples of parameters for which we prove normal or log-normal limit laws.