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Distinguishing Different Types of Inhomogeneity in Neyman–Scott Point Processes

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  • T. Mrkvička

    (University of South Bohemia
    Biology Center of the Academy of Sciences of the Czech Republic)

Abstract

In this paper we introduce a graphical and formal approach to distinguishing different typed of inhomogeneity on Neyman–Scott point processes. The assumed types of inhomogeneity are (1) inhomogeneous cluster centers, (2) second order intensity reweighted stationarity, (3) location dependent scaling and a new type (4) growing clusters. The performance of the method is studied via a simulation study. This work has been motivated and illustrated by ecological studies of the spatial distribution of fish in an inland reservoir.

Suggested Citation

  • T. Mrkvička, 2014. "Distinguishing Different Types of Inhomogeneity in Neyman–Scott Point Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 385-395, June.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-013-9365-4
    DOI: 10.1007/s11009-013-9365-4
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    1. Jesper Møller & Rasmus P. Waagepetersen, 2007. "Modern Statistics for Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 643-684, December.
    2. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    3. Rasmus Plenge Waagepetersen, 2007. "An Estimating Function Approach to Inference for Inhomogeneous Neyman–Scott Processes," Biometrics, The International Biometric Society, vol. 63(1), pages 252-258, March.
    4. Rasmus Waagepetersen & Yongtao Guan, 2009. "Two‐step estimation for inhomogeneous spatial point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 685-702, June.
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