Essec\Faculty\Model\Contribution {#2216
  #_index: "academ_contributions"
  #_id: "781"
  #_source: array:26 [
    "id" => "781"
    "slug" => "chord-length-distribution-functions-and-rice-formulae-application-to-random-media"
    "yearMonth" => "2012-09"
    "year" => "2012"
    "title" => "Chord-Length Distribution Functions and Rice Formulae. Application to Random Media"
    "description" => "ESTRADE, A., IRIBARREN, I. et KRATZ, M. (2012). Chord-Length Distribution Functions and Rice Formulae. Application to Random Media. <i>Extremes</i>, 15(3), pp. 333-352."
    "authors" => array:3 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
      1 => array:1 [
        "name" => "ESTRADE A."
      ]
      2 => array:1 [
        "name" => "IRIBARREN I."
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:7 [
      0 => "Chord"
      1 => "(Up/down) crossing"
      2 => "Gaussian process"
      3 => "Level-cut process"
      4 => "Palm probability"
      5 => "Porous medium"
      6 => "Rice formula"
    ]
    "updatedAt" => "2021-02-02 16:16:18"
    "publicationUrl" => "https://link.springer.com/article/10.1007/s10687-011-0141-y"
    "publicationInfo" => array:3 [
      "pages" => "333-352"
      "volume" => "15"
      "number" => "3"
    ]
    "type" => array:2 [
      "fr" => "Articles"
      "en" => "Journal articles"
    ]
    "support_type" => array:2 [
      "fr" => "Revue scientifique"
      "en" => "Scientific journal"
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => "We consider a stationary and isotropic bi-phasic (pore and solid) medium, draw many lines through it, and see each line as a one-dimensional level-cut process with value 0 or 1 according to whether a regular stationary process X is less or greater than a given level. The intervals corresponding to the points at which X is in a given phase are named chords. We are interested in obtaining information on the chord-length distribution functions. Working with the Palm probability measure and using level crossings techniques, in particular, Rice methods, we can obtain not only the exact analytical formula of the chord-length distribution function but also the joint distribution function of the lengths of two successive chords. Finally, we indicate some concrete applications for the computation of usual stereological parameters."
      "en" => "We consider a stationary and isotropic bi-phasic (pore and solid) medium, draw many lines through it, and see each line as a one-dimensional level-cut process with value 0 or 1 according to whether a regular stationary process X is less or greater than a given level. The intervals corresponding to the points at which X is in a given phase are named chords. We are interested in obtaining information on the chord-length distribution functions. Working with the Palm probability measure and using level crossings techniques, in particular, Rice methods, we can obtain not only the exact analytical formula of the chord-length distribution function but also the joint distribution function of the lengths of two successive chords. Finally, we indicate some concrete applications for the computation of usual stereological parameters."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-12-03T17:21:44.000Z"
    "docTitle" => "Chord-Length Distribution Functions and Rice Formulae. Application to Random Media"
    "docSurtitle" => "Journal articles"
    "authorNames" => "<a href="/cv/kratz-marie">KRATZ Marie</a>, ESTRADE A., IRIBARREN I."
    "docDescription" => "<span class="document-property-authors">KRATZ Marie, ESTRADE A., IRIBARREN I.</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2012</span>"
    "keywordList" => "<a href="#">Chord</a>, <a href="#">(Up/down) crossing</a>, <a href="#">Gaussian process</a>, <a href="#">Level-cut process</a>, <a href="#">Palm probability</a>, <a href="#">Porous medium</a>, <a href="#">Rice formula</a>"
    "docPreview" => "<b>Chord-Length Distribution Functions and Rice Formulae. Application to Random Media</b><br><span>2012-09 | Journal articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://link.springer.com/article/10.1007/s10687-011-0141-y" target="_blank">Chord-Length Distribution Functions and Rice Formulae. Application to Random Media</a>"
  ]
  +lang: "en"
  +"_type": "_doc"
  +"_score": 9.19509
  +"parent": null
}