ERIC Number: EJ818206
Record Type: Journal
Publication Date: 2008-May
Abstractor: As Provided
Reference Count: 12
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.
Descriptors: Heuristics, Computation, Probability, Physics, Measurement, Mathematical Concepts, Theories, Equations (Mathematics), Science Instruction
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Authoring Institution: N/A