IDEAS home Printed from
   My bibliography  Save this article

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


  • Ahmad, Ola
  • Pinoli, Jean-Charles


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

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:559-567. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.