Essec\Faculty\Model\Contribution {#2216
  #_index: "academ_contributions"
  #_id: "9759"
  #_source: array:26 [
    "id" => "9759"
    "slug" => "rate-of-poisson-approximation-of-the-number-of-exceedances-of-nonstationary-normal-sequences"
    "yearMonth" => "1995-05"
    "year" => "1995"
    "title" => "Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences"
    "description" => "KRATZ, M. et HÜSLER, J. (1995). Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences. <i>Stochastic Processes and their Applications</i>, 55, pp. 301-313."
    "authors" => array:2 [
      0 => array:3 [
        "name" => "KRATZ Marie"
        "bid" => "B00072305"
        "slug" => "kratz-marie"
      ]
      1 => array:1 [
        "name" => "HÜSLER Jürg"
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:4 [
      0 => "AMS classification -Stein-Chen approximation"
      1 => "rate of convergence"
      2 => "exceedances -maxima"
      3 => "nonstationary Gaussian sequences"
    ]
    "updatedAt" => "2021-07-13 14:31:20"
    "publicationUrl" => null
    "publicationInfo" => array:3 [
      "pages" => "301-313"
      "volume" => "55"
      "number" => null
    ]
    "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" => "It is known that the partial maximum of nonstationary Gaussian sequences converges in distribution and that the number of exceedances of a boundary is asymptotically a Poisson random variable, under certain restrictions. We investigate the rate of Poisson approximation for the number of exceedances. We generalize the result known in the stationary case, showing that the given bound of the rate depends on the largest positive auto-correlation value (less than 1) and the lowest values of the nonconstant boundary. We show that for special cases this bound cannot be improved."
      "en" => "It is known that the partial maximum of nonstationary Gaussian sequences converges in distribution and that the number of exceedances of a boundary is asymptotically a Poisson random variable, under certain restrictions. We investigate the rate of Poisson approximation for the number of exceedances. We generalize the result known in the stationary case, showing that the given bound of the rate depends on the largest positive auto-correlation value (less than 1) and the lowest values of the nonconstant boundary. We show that for special cases this bound cannot be improved."
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2024-11-21T12:21:46.000Z"
    "docTitle" => "Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences"
    "docSurtitle" => "Journal articles"
    "authorNames" => "<a href="/cv/kratz-marie">KRATZ Marie</a>, HÜSLER Jürg"
    "docDescription" => "<span class="document-property-authors">KRATZ Marie, HÜSLER Jürg</span><br><span class="document-property-authors_fields">Information Systems, Data Analytics and Operations</span> | <span class="document-property-year">1995</span>"
    "keywordList" => "<a href="#">AMS classification -Stein-Chen approximation</a>, <a href="#">rate of convergence</a>, <a href="#">exceedances -maxima</a>, <a href="#">nonstationary Gaussian sequences</a>"
    "docPreview" => "<b>Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences</b><br><span>1995-05 | Journal articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="#" target="_blank">Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences</a>"
  ]
  +lang: "en"
  +"_type": "_doc"
  +"_score": 8.816764
  +"parent": null
}