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Generalization of a Nearest Neighbor Measure of Dispersion for Use in K Dimensions
Author(s) -
Clark Philip J.,
Evans Francis C.
Publication year - 1979
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.2307/1937660
Subject(s) - measure (data warehouse) , mathematics , generalization , k nearest neighbors algorithm , dispersion (optics) , statistics , space (punctuation) , statistical physics , population , index of dispersion , mathematical analysis , physics , optics , computer science , demography , artificial intelligence , poisson regression , database , sociology , operating system
The 1st, 2nd and 3rd moments of r, the distance to nearest neighbor, are derived so as to generalize for use in k dimensions a measure of spacing based on the ratio of the mean distance observed in a population of known density to the mean distance expected under the assumption of random dispersion. Numerical values of these moments for 1—, 2—, and 3—dimensional space are presented, and significance tests for the difference between observed and expected mean distances are considered.