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The K‐Function for Nearly Regular Point Processes

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  • Charles C. Taylor
  • Ian L. Dryden
  • Rahman Farnoosh

Abstract

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.

Suggested Citation

  • Charles C. Taylor & Ian L. Dryden & Rahman Farnoosh, 2001. "The K‐Function for Nearly Regular Point Processes," Biometrics, The International Biometric Society, vol. 57(1), pages 224-231, March.
    • Handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:224-231
    DOI: 10.1111/j.0006-341X.2001.00224.x
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    1. A. J. Baddeley & R. A. Moyeed & C. V. Howard & A. Boyde, 1993. "Analysis of a Three‐Dimensional Point Pattern with Replication," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(4), pages 641-668, December.
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