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On the linear combination of the Gaussian and student’s t random field and the integral geometry of its excursion sets


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  • Ahmad, Ola
  • Pinoli, Jean-Charles
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    In this paper, a random field, denoted by GTβν, is defined from the linear combination of two independent random fields, one is a Gaussian random field and the second is a student’s t random field with ν degrees of freedom scaled by β. The goal is to give the analytical expressions of the expected Euler–Poincaré characteristic of the GTβν excursion sets on a compact subset S of R2. The motivation comes from the need to model the topography of 3D rough surfaces represented by a 3D map of correlated and randomly distributed heights with respect to a GTβν random field. The analytical and empirical Euler–Poincaré characteristics are compared in order to test the GTβν model on the real surface.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 2 ()
    Pages: 559-567

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:559-567

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    Keywords: Gaussian random field; Student’s t random field; Excursion sets; Minkowski functionals; Euler–Poincaré characteristic;


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