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On the higher order product density functions of a Neyman–Scott cluster point process

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  • Jalilian, Abdollah

Abstract

A general formula and upper bounds for the intensity-reweighted product density functions of Neyman–Scott processes are obtained. Analytical expressions are presented for the intensity-reweighted product and cumulant densities of the Thomas process, an important special case of Neyman–Scott processes.

Suggested Citation

  • Jalilian, Abdollah, 2016. "On the higher order product density functions of a Neyman–Scott cluster point process," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 144-150.
    • Handle: RePEc:eee:stapro:v:117:y:2016:i:c:p:144-150
    DOI: 10.1016/j.spl.2016.05.003
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. D. Stoyan & U. Bertram & H. Wendrock, 1993. "Estimation variances for estimators of product densities and pair correlation functions of planar point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 211-221, June.
    5. K. Schladitz & A. J. Baddeley, 2000. "A Third Order Point Process Characteristic," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 657-671, December.
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    Cited by:

    1. Abdollah Jalilian & Jorge Mateu, 2023. "Assessing similarities between spatial point patterns with a Siamese neural network discriminant model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 21-42, March.

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