The Mean Distance to the n-th Neighbour in a Uniform Distribution of Random Points: An Application of Probability Theory
| dc.creator | Bhattacharyya, Pratip | |
| dc.creator | Chakrabarti, Bikas K. | |
| dc.date | 2002-12-17 | |
| dc.date | 2003-09-17 | |
| dc.date.accessioned | 2026-07-07T04:53:51Z | |
| dc.date.available | 2026-07-07T04:53:51Z | |
| dc.description | We study different ways of determining the mean distance $ < r_n >$ between a reference point and its $n$-th neighbour among random points distributed with uniform density in a $D$-dimensional Euclidean space. First we present a heuristic method; though this method provides only a crude mathematical result, it shows a simple way of estimating $ < r_n >$. Next we describe two alternative means of deriving the exact expression of $<r_n>$: we review the method using absolute probability and develop an alternative method using conditional probability. Finally we obtain an approximation to $ < r_n >$ from the mean volume between the reference point and its $n$-th neighbour and compare it with the heuristic and exact results. | |
| dc.description | 6 pages (REVTex4), minor changes in content, typing errors corrected, references added | |
| dc.identifier | https://arxiv.org/abs/math/0212230 | |
| dc.identifier | http://arxiv.org/abs/math/0212230 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66014 | |
| dc.subject | Probability | |
| dc.subject | Data Analysis, Statistics and Probability | |
| dc.title | The Mean Distance to the n-th Neighbour in a Uniform Distribution of Random Points: An Application of Probability Theory | |
| dc.type | text |