论文标题
间隔捕获Digraph家族的统治数及其用于测试均匀性的使用
Domination Number of an Interval Catch Digraph Family and its use for Testing Uniformity
论文作者
论文摘要
我们考虑在随机环境中使用一种特殊类型的间隔捕获挖掘（ICD）家族，以用于一维数据，并提出其用于测试均匀性的使用。这些ICD由扩展和中心性参数定义，因此我们将此ICD称为参数化ICD（PICD）。当该PICD家族的主导数量从一个均匀（和不统一）的分布中的整个参数范围内的均匀（和非统一）分布时，我们得出了该PICD家族的统治数的确切（和渐近）分布。从而确定渐近分布是非分类的参数。在某些参数组合的渐近分布中，我们观察到跳跃（从退化到非分布到非分布到另一个分布）。我们使用统治数来测试实际线路的数据均匀性，证明其对某些替代方案的一致性，并将其与两种常用的测试和三个最近提出的文献测试以及该ICD的三个最近提出的测试以及另一个ICD家族的大小和力量。根据我们广泛的蒙特卡洛模拟，我们证明了与其他测试相比，PICD的支配数对于某些类型的均匀性具有更高的功率。
We consider a special type of interval catch digraph (ICD) family for one-dimensional data in a randomized setting and propose its use for testing uniformity. These ICDs are defined with an expansion and a centrality parameter, hence we will refer to this ICD as parameterized ICD (PICD). We derive the exact (and asymptotic) distribution of the domination number of this PICD family when its vertices are from a uniform (and non-uniform) distribution in one dimension for the entire range of the parameters; thereby determine the parameters for which the asymptotic distribution is non-degenerate. We observe jumps (from degeneracy to non-degeneracy or from a non-degenerate distribution to another) in the asymptotic distribution of the domination number at certain parameter combinations. We use the domination number for testing uniformity of data in real line, prove its consistency against certain alternatives, and compare it with two commonly used tests and three recently proposed tests in literature and also arc density of this ICD and of another ICD family in terms of size and power. Based on our extensive Monte Carlo simulations, we demonstrate that domination number of our PICD has higher power for certain types of deviations from uniformity compared to other tests.
