任意凸多面体上布点均匀性的度量  

Measure of Uniformity of Points Distributed in a General Convex Polyhedron

作　　者：王艳云[1] 唐煜[1] 

机构地区：[1]苏州大学数学科学学院,苏州215006

出　　处：《应用数学学报》2009年第5期849-857,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10626038;10801104)资助项目

摘　　要：均匀性度量是构作均匀设计的基础,本文从距离概念出发,通过对称的方法,得到一种新的距离函数—势函数,并将势函数作为衡量任意凸多面体上布点均匀性好坏的准则.数值例子和多变量Kendall协和系数检验表明,当试验区域限制在单位立方体上时,势函数与目前常用的两种偏差-中心化L_2-偏差和可卷L_2-偏差在度量布点均匀性方面结论一致.Measure of uniformity is essential for constructing uniform design. Based on the distance concept, one kind of new distance function--potential function is introduced and used to measure the uniformity of points distributed in a general convex polyhedron. Numerical examples and multivariate Kendall concordance coefficient of multivariate test indicate when the experimental region is limited to the unit cube, potential function is consistent with centered L2- discrepancy and wrap-around L2-discrepancy which are often used to measure uniformity in existing literatures.

关 键 词：试验设计 均匀性度量 对称 势函数 

分 类 号：O212.6[理学—概率论与数理统计]