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Computation of Coverage Probabilities in a Spherical Germ-Grain Model

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  • Ian Flint

    (Nanyang Technological University)

  • Nicolas Privault

    (Nanyang Technological University)

Abstract

We consider a spherical germ-grain model on ℝ d $\mathbb {R}^{d}$ in which the centers of the spheres are driven by a possibly non-Poissonian point process. We show that various covering probabilities can be expressed using the cumulative distribution function of the random radii on one hand, and distances to certain subsets of ℝ d $\mathbb {R}^{d}$ on the other hand. This result allows us to compute the spherical and linear contact distribution functions, and to derive expressions which are suitable for numerical computation. Determinantal point processes are an important class of examples for which the relevant quantities take the form of Fredholm determinants.

Suggested Citation

  • Ian Flint & Nicolas Privault, 2021. "Computation of Coverage Probabilities in a Spherical Germ-Grain Model," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 491-502, June.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:2:d:10.1007_s11009-019-09741-5
    DOI: 10.1007/s11009-019-09741-5
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    References listed on IDEAS

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    1. Frédéric Lavancier & Jesper Møller & Ege Rubak, 2015. "Determinantal point process models and statistical inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(4), pages 853-877, September.
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