Barbour, Andrew D; Xia, A (2001). The number of two-dimensional maxima. Advances in Applied Probability, 33(4):727-750.
Let n points be placed uniformly at random in a subset A of the plane. A point is said to be maximal in the configuration if no other point is larger in both coordinates. We show that, for large n and for many sets A, the number of maximal points is approximately normally distributed. The argument uses Stein's method, and is also applicable in higher dimensions.
Let n points be placed uniformly at random in a subset A of the plane. A point is said to be maximal in the configuration if no other point is larger in both coordinates. We show that, for large n and for many sets A, the number of maximal points is approximately normally distributed. The argument uses Stein's method, and is also applicable in higher dimensions.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Statistics and Probability
Physical Sciences > Applied Mathematics |
| Uncontrolled Keywords: | Maximal points, Stein's method, record values, Johnson-Mehl process |
| Language: | English |
| Date: | 2001 |
| Deposited On: | 07 Apr 2010 12:26 |
| Last Modified: | 03 Dec 2023 02:41 |
| Publisher: | Cambridge University Press |
| ISSN: | 0001-8678 |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1239/aap/1011994025 |
Barbour, Andrew D