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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

Abstract

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.

Suggested Citation

  • Ahmad, Ola & Pinoli, Jean-Charles, 2013. "On the linear combination of the Gaussian and student’s t random field and the integral geometry of its excursion sets," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 559-567.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:559-567
    DOI: 10.1016/j.spl.2012.10.022
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