| Автор | R H C Lopes |
| Автор | P R Hobson |
| Автор | I D Reid |
| Дата выпуска | 2008-07-01 |
| dc.description | Goodness-of-fit statistics measure the compatibility of random samples against some theoretical or reference probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a non-parametric statistic for comparing two empirical distributions which defines the largest absolute difference between the two cumulative distribution functions as a measure of disagreement. Adapting this test to more than one dimension is a challenge because there are 2<sup>d</sup>-1 independent ways of ordering a cumulative distribution function in d dimensions. We discuss Peacock's version of the Kolmogorov-Smirnov test for two-dimensional data sets which computes the differences between cumulative distribution functions in 4n<sup>2</sup> quadrants. We also examine Fasano and Franceschini's variation of Peacock's test, Cooke's algorithm for Peacock's test, and ROOT's version of the two-dimensional Kolmogorov-Smirnov test. We establish a lower-bound limit on the work for computing Peacock's test of Ω(n<sup>2</sup>lgn), introducing optimal algorithms for both this and Fasano and Franceschini's test, and show that Cooke's algorithm is not a faithful implementation of Peacock's test. We also discuss and evaluate parallel algorithms for Peacock's test. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Копирайт | © 2008 IOP Publishing Ltd |
| Название | Computationally efficient algorithms for the two-dimensional Kolmogorov–Smirnov test |
| Тип | paper |
| DOI | 10.1088/1742-6596/119/4/042019 |
| Electronic ISSN | 1742-6596 |
| Print ISSN | 1742-6588 |
| Журнал | Journal of Physics: Conference Series |
| Том | 119 |
| Первая страница | 42019 |
| Последняя страница | 42027 |
| Аффилиация | R H C Lopes; School of Engineering and Design, Brunel University, Uxbridge UB8 3PH, UK |
| Аффилиация | P R Hobson; School of Engineering and Design, Brunel University, Uxbridge UB8 3PH, UK |
| Аффилиация | I D Reid; School of Engineering and Design, Brunel University, Uxbridge UB8 3PH, UK |
| Выпуск | 4 |
