Nearest neighbor analysis in one dimension

Technical Report · Wed Feb 01 04:00:00 EST 1995

DOI:https://doi.org/10.2172/33152· OSTI ID:33152

Weingart, M; Selvin, S

Since its initial presentation by Clark and Evans, nearest neighbor analysis for spatial randomness has gained considerable popularity in fields as diverse as geography, ecology, archaeology, cell biology, forestry, meteorology, and epidemiology. Epidemiologists are often interested in determining whether disease cases are clustered, dispersed, or randomly distributed, since different patterns of disease incidence over time or space can provide dues to the etiology of the disease. An environmental hazard or a transmissable agent can produce a cluster of disease events, i.e. a set of events occurring unusually dose to each other in time, space, or both time and space. In spite of its wide applicability, few attempts have been made to adapt the nearest neighbor method to the analysis of points distributed along a line. This report outlines the theoretical derivation of the moments of the mean nearest neighbor distance in the one dimension case and the correction of its expected value in order to overcome the boundary problem. It presents the derivation of the moments of order statistics, for specific sample sizes and for the general case. These results are then used for the derivation of the moments of nearest neighbor distances, and for the derivation of the moments of the mean nearest neighbor distance. Then the boundary problem and an examination of five alternative ways to compensate for it in the calculation of the expected value of the mean nearest neighbor distance are discussed. Finally, the results from a large scale computer simulation which compares the various correction methods are presented.

• Research Organization: Lawrence Berkeley Lab., CA (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 33152
• Report Number(s): LBL--36888; ON: DE95009378
• Country of Publication: United States
• Language: English

Related Subjects

55 BIOLOGY AND MEDICINE
BASIC STUDIES
99 GENERAL AND MISCELLANEOUS
COMPUTER CALCULATIONS
EPIDEMIOLOGY
MATHEMATICAL MODELS
ONE-DIMENSIONAL CALCULATIONS
RANDOMNESS