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

Ola Suleiman Ahmad (1, 2, 3, 4) , Jean-Charles Pinoli (1, 2, 3, 4)

1 LGF-ENSMSE - Laboratoire Georges Friedel
2 CIS-ENSMSE - Centre Ingénierie et Santé
3 STBio-ENSMSE - Surfaces et Tissus Biologiques
4 IFRESIS - Institut Fédératif de Recherche en Sciences et Ingénierie de la Santé

In this paper, a random field, denoted by GT_β^ν, 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 v degrees of freedom scaled by β. The goal is to give the analytical expressions of the expected Euler-Poincaré characteristic of the GT_β^ν 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 GT_β^ν random field. The analytical and empirical Euler-Poincaré characteristics are compared in order to test the GT_β^ν model on the real surface.

Mots clés: Gaussian random field; Student's <i>t</i> random field; Excursion sets; Minkowski functionals; Euler-Poincaré characteristic

Domaines: Génie des procédés; Statistiques [math.ST]; Théorie [stat.TH]

Ola Suleiman Ahmad, Jean-Charles Pinoli. On the linear combination of the Gaussian and student's t random field and the integral geometry of its excursion sets. Statistics and Probability Letters, 2013, 83, pp.559-567. ⟨10.1016/j.spl.2012.10.022⟩. ⟨hal-00819094⟩