Bhattacharyya, Pratip ; Chakrabarti, Bikas K. (2008) The mean distance to the nth neighbour in a uniform distribution of random points: an application of probability theory European Journal of Physics, 29 (3). 639_1-639_6. ISSN 0143-0807
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Official URL: http://iopscience.iop.org/0143-0807/29/3/023
Related URL: http://dx.doi.org/10.1088/0143-0807/29/3/023
Abstract
We study different ways of determining the mean distance <rn> 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 <rn>. Next, we describe two alternative means of deriving the exact expression of <rn> we review the method using absolute probability and develop an alternative method using conditional probability. Finally, we obtain an approximation to <rn> from the mean volume between the reference point and its nth neighbour and compare it with the heuristic and exact results.
Item Type: | Article |
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Source: | Copyright of this article belongs to Institute of Physics. |
Keywords: | Mathematics; Probability Physics; Data Analysis; Statistics; Probability |
ID Code: | 44813 |
Deposited On: | 23 Jun 2011 07:57 |
Last Modified: | 23 Jun 2011 07:57 |
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