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ERIC Number: EJ818206
Record Type: Journal
Publication Date: 2008-May
Pages: 7
Abstractor: As Provided
Reference Count: 12
ISBN: N/A
ISSN: ISSN-0143-0807
The Mean Distance to the nth Neighbour in a Uniform Distribution of Random Points: An Application of Probability Theory
Bhattacharyya, Pratip; Chakrabarti, Bikas K.
European Journal of Physics, v29 n3 p639-645 May 2008
We study different ways of determining the mean distance (r[subscript n]) between a reference point and its nth 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[subscript n]). Next, we describe two alternative means of deriving the exact expression of (r[subscript n]): we review the method using absolute probability and develop an alternative method using conditional probability. Finally, we obtain an approximation to (r[subscript n]) from the mean volume between the reference point and its nth neighbour and compare it with the heuristic and exact results.
Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A