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The K ‐Function for Nearly Regular Point Processes
Author(s) -
Taylor Charles C.,
Dryden Ian L.,
Farnoosh Rahman
Publication year - 2001
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2001.00224.x
Subject(s) - equilateral triangle , estimator , point process , mathematics , gaussian , grid , benchmark (surveying) , point (geometry) , function (biology) , square (algebra) , gaussian process , statistics , mathematical optimization , algorithm , geometry , physics , geodesy , quantum mechanics , evolutionary biology , biology , geography
Summary. We propose modeling a nearly regular point pattern by a generalized Neyman‐Scott process in which the offspring are Gaussian perturbations from a regular mean configuration. The mean configuration of interest is an equilateral grid, but our results can be used for any stationary regular grid. The case of uniformly distributed points is first studied as a benchmark. By considering the square of the interpoint distances, we can evaluate the first two moments of the K‐function. These results can be used for parameter estimation, and simulations are used to both verify the theory and to assess the accuracy of the estimators. The methodology is applied to an investigation of regularity in plumes observed from swimming microorganisms.