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A Bivariate Cramér–Von Mises Type of Test for Spatial Randomness
Author(s) -
Zimmerman Dale L.
Publication year - 1993
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347408
Subject(s) - mathematics , bivariate analysis , anderson–darling test , statistics , type (biology) , randomness , econometrics , kolmogorov–smirnov test , statistical hypothesis testing , geology , paleontology
SUMMARY A test for the randomness of a mapped spatial pattern of events in a rectangle D in R 2 is examined that is based on the ‘distance’ between the bivariate empirical distribution function of the events' Cartesian co‐ordinates and the uniform distribution function. The distance between distribution functions is measured by a modification of the bivariate Cramér–von Mises statistic that is invariant to the corner of D identified as the origin. This invariance property, which is essential, is lacking in the standard bivariate Cramér–von Mises statistic. Several real examples and results from simulation indicate that the test proposed is superior to existing tests for detecting heterogeneous alternatives to spatial randomness but inferior for detecting regular or aggregated alternatives. Some additional features of the test are its computational simplicity, the non‐necessity of adjusting for edge effects and the ease with which it can be extended to test for certain types of heterogeneity.