APPROXIMATIONS FOR TAIL PROBABILITIES AND MOMENTS OF THE SCAN STATISTIC

被引：13

作者：

GLAZ, J ^{[1
]}

机构：

[1] UNIV CONNECTICUT,DEPT STAT,STORRS,CT 06269

来源：

COMPUTATIONAL STATISTICS & DATA ANALYSIS | 1992年 / 14卷 / 02期

关键词：

BONFERRONI-TYPE INEQUALITIES; CLUSTERING PROBABILITIES; DISTRIBUTION OF THE SMALLEST INTERVAL; PRODUCT-TYPE APPROXIMATIONS; SCANNING WINDOW;

D O I：

10.1016/0167-9473(92)90175-F

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

The scan statistic is used in many areas of science to test the null hypothesis of uniformity against a clustering alternative. In this article product-type approximations and Bonferroni-type upper bounds are derived for the tail probabilities of the scan statistic. These new approximations appear to be remarkably accurate and are utilized to compute approximations for the expected size and the standard deviation of the scan statistic. Moreover, accurate approximations are obtained for the distribution and the moments of the smallest interval containing m ordered observations from a uniform distribution in (0, 1]. A simulation study is carried out to evaluate the approximations derived in this article.

引用

页码：213 / 227

页数：15

共 25 条

[1]

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[2]

[Anonymous], 1968, INTRO PROBABILITY TH

[3]

BARTON DE, 1956, J ROY STAT SOC B, V18, P79

[4] A USEFUL UPPER BOUND FOR THE TAIL PROBABILITIES OF THE SCAN STATISTIC WHEN THE SAMPLE-SIZE IS LARGE [J].