{
  "id": "1306.5294",
  "version": "v2",
  "published": "2013-06-22T06:26:46.000Z",
  "updated": "2013-09-04T15:47:20.000Z",
  "title": "A Note on Computing Extreme Tail Probabilities of the Noncentral T Distribution with Large Noncentrality Parameter",
  "authors": [
    "Viktor Witkovsky"
  ],
  "comment": "Preprint submitted to Acta Universitatis Palackianae Olomucensis, Facultas rerum naturalium, Mathematica, submitted June 21, 2013, revised September 4, 2013",
  "categories": [
    "stat.CO"
  ],
  "abstract": "The noncentral $t$-distribution is a generalization of the Student's $t$-distribution. In this paper we suggest an alternative approach for computing the cumulative distribution function (CDF) of the noncentral $t$-distribution which is based on a direct numerical integration of a well behaved function. With a double-precision arithmetic, the algorithm provides highly precise and fast evaluation of the extreme tail probabilities of the noncentral $t$-distribution, even for large values of the noncentrality parameter $\\delta$ and the degrees of freedom $\\nu$. The implementation of the algorithm is available at the MATLAB Central, File Exchange: http://www.mathworks.com/matlabcentral/fileexchange/41790-nctcdfvw.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-04T15:47:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62E15",
      "62-04"
    ],
    "keywords": [
      "computing extreme tail probabilities",
      "large noncentrality parameter",
      "distribution",
      "matlab central",
      "large values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.5294W"
    }
  }
}