Essec\Faculty\Model\Contribution {#2216 ▼
#_index: "academ_contributions"
#_id: "781"
#_source: array:26 [
"id" => "781"
"slug" => "781-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. 
ESTRADE, A., IRIBARREN, I. et KRATZ, M. (2012). Chord-Length Distribution Functions and Rice Formula "
"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. We consider a stationary and isotropic bi-phasic (pore and solid) medium, draw many lines through it "
"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. We consider a stationary and isotropic bi-phasic (pore and solid) medium, draw many lines through it "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-03-20T22:21:45.000Z"
"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> <span class="document-property-authors">KRATZ Marie, ESTRADE A., IRIBARREN I.</span><br><span class= "
"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> <a href="#">Chord</a>, <a href="#">(Up/down) crossing</a>, <a href="#">Gaussian process</a>, <a href "
"docPreview" => "<b>Chord-Length Distribution Functions and Rice Formulae. Application to Random Media</b><br><span>2012-09 | Journal articles </span> <b>Chord-Length Distribution Functions and Rice Formulae. Application to Random Media</b><br><span>2 "
"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> <a href="https://link.springer.com/article/10.1007/s10687-011-0141-y" target="_blank">Chord-Length D "
]
+lang: "en"
+"_type": "_doc"
+"_score": 9.273628
+"parent": null
}
