Essec\Faculty\Model\Contribution {#2190`
#_index: "academ_contributions"
#_id: "781"
#_source: array:25 [``
"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, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
`]
"indexedAt" => "2023-12-10T20:22:04.000Z"
"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, Decision Sciences and Statistics</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"
]
+lang: "en"
+"_type": "_doc"
+"_score": 9.129347
+"parent": null
}