Essec\Faculty\Model\Contribution {#2216
  #_index: "academ_contributions"
  #_id: "6776"
  #_source: array:26 [
    "id" => "6776"
    "slug" => "on-the-decay-of-chord-lengths"
    "yearMonth" => "2009-07"
    "year" => "2009"
    "title" => "On the decay of Chord-lengths"
    "description" => "KRATZ, M. (2009). On the decay of Chord-lengths. Dans: Stochastic Processes and their Applications."
    "authors" => array:1 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
    ]
    "ouvrage" => "Stochastic Processes and their Applications"
    "keywords" => array:1 [
      0 => "Chord-length"
    ]
    "updatedAt" => "2021-04-19 17:57:25"
    "publicationUrl" => null
    "publicationInfo" => array:3 [
      "pages" => null
      "volume" => null
      "number" => null
    ]
    "type" => array:2 [
      "fr" => "Communications dans une conférence"
      "en" => "Presentations at an Academic or Professional conference"
    ]
    "support_type" => array:2 [
      "fr" => null
      "en" => null
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => "The modelling of  random bi-phasic or porous media (bones, stones, ...) has been, and still is, subject to investigation by mathematicians, physicists or physicians.  Here, we consider a thresholded random process X as a model, and look for information through the intervals when X is in a given phase, named chords.  We focus on the study of the chord-length tail distribution function. In the literature, different types of tail's behavior have been observed, among which exponential or power like decay. In this work, we look for the link between those two possible types of decay for the chord-length tail distribution function and the covariance function of X. First we perform with no  a priori on the chord-length tail's behavior, a statistical analysis on simulated data, using the Mean Excess Plot method as a graphical method to discriminate between  light or heavy tails, and estimating the shape parameter of the associated GPD of the tail. Then we provide theoretical results proving on one hand the exponential decay of the chord-length tail distribution function when considering exponentially decreasing covariance function of a stationary Gaussian process , on the other hand, a decay faster than any negative power function  when considering a r-mixing process X. Joint work with Y. Demichel, A. Estrade and G. Samorodnitsky"
      "en" => "The modelling of  random bi-phasic or porous media (bones, stones, ...) has been, and still is, subject to investigation by mathematicians, physicists or physicians.  Here, we consider a thresholded random process X as a model, and look for information through the intervals when X is in a given phase, named chords.  We focus on the study of the chord-length tail distribution function. In the literature, different types of tail's behavior have been observed, among which exponential or power like decay. In this work, we look for the link between those two possible types of decay for the chord-length tail distribution function and the covariance function of X. First we perform with no  a priori on the chord-length tail's behavior, a statistical analysis on simulated data, using the Mean Excess Plot method as a graphical method to discriminate between  light or heavy tails, and estimating the shape parameter of the associated GPD of the tail. Then we provide theoretical results proving on one hand the exponential decay of the chord-length tail distribution function when considering exponentially decreasing covariance function of a stationary Gaussian process , on the other hand, a decay faster than any negative power function  when considering a r-mixing process X. Joint work with Y. Demichel, A. Estrade and G. Samorodnitsky"
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-12-22T00:21:50.000Z"
    "docTitle" => "On the decay of Chord-lengths"
    "docSurtitle" => "Presentations at an Academic or Professional conference"
    "authorNames" => "<a href="/cv/kratz-marie">KRATZ Marie</a>"
    "docDescription" => "<span class="document-property-authors">KRATZ Marie</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">2009</span>"
    "keywordList" => "<a href="#">Chord-length</a>"
    "docPreview" => "<b>On the decay of Chord-lengths</b><br><span>2009-07 | Presentations at an Academic or Professional conference </span>"
    "docType" => "research"
    "publicationLink" => "<a href="#" target="_blank">On the decay of Chord-lengths</a>"
  ]
  +lang: "en"
  +"_type": "_doc"
  +"_score": 9.178505
  +"parent": null
}