非均匀一维数据的类覆盖捕捉有向图的控制数分布
The Distribution of the Domination Number of Class Cover Catch Digraphs for Non-uniform One-dimensional Data
摘要：
对于具有$d \ge 1$的$\R^d$中的两个或更多个点类，可以使用来自一个类的点相对于来自另一个类的点的相对位置来构造类覆盖捕获有向图（CCCD）。CCCD由Priebe、DeVinney和Mar-chette（2001年）介绍。关于随机类catch覆盖有向图的控制数分布。Statistics and Probability Letters，55：239-246），他们调查了两个类$\X$和$\Y$的情况。他们基于相对于$\Y$点的$\X$点计算了CCCD控制数的精确（有限样本）分布，这两个点都在有界区间上均匀分布。我们研究了基于区间上非均匀$\X$点的数据的CCCD控制数的分布，该区间的端点来自$\Y$。然后，我们将这些计算扩展到有界区间上的多个$\Y$点。
英文摘要：
For two or more classes of points in $\R^d$ with $d \ge 1$, the class cover catch digraphs (CCCDs) can be constructed using the relative positions of the points from one class with respect to the points from the other class. The CCCDs were introduced by (Priebe, DeVinney, and Mar-chette, (2001). On the distribution of the domination number of random class catch cover di-graphs. Statistics and Probability Letters, 55:239-246) who investigated the case of two classes, $\X$ and $\Y$. They calculated the exact (finite sample) distribution of the domination number of the CCCDs based on $\X$ points relative to $\Y$ points both of which were uniformly distri-buted on a bounded interval. We investigate the distribution of the domination number of the CCCDs based on data from non-uniform $\X$ points on an interval with end points from $\Y$. Then we extend these calculations for multiple $\Y$ points on bounded intervals.
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