{
  "id": "1406.0005",
  "version": "v3",
  "published": "2014-05-30T20:00:06.000Z",
  "updated": "2014-08-19T19:43:50.000Z",
  "title": "Exact computation of the CDF of the Euclidean distance between a point and a random variable uniformly distributed in disks, balls, or polyhedrons and application to PSHA",
  "authors": [
    "Vincent Guigues"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a random variable expressed as the Euclidean distance between an arbitrary point and a random variable uniformly distributed in a closed and bounded set of a three-dimensional Euclidean space. Four cases are considered for this set: a union of disjoint disks, a union of disjoint balls, a union of disjoint line segments, and the boundary of a polyhedron. In the first three cases, we provide closed-form expressions of the cumulative distribution function and the density. In the last case, we propose an algorithm with complexity O(n ln n), n being the number of edges of the polyhedron, that computes exactly the cumulative distribution function. An application of these results to probabilistic seismic hazard analysis and extensions are discussed.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-08-19T19:43:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "65D99",
      "51N20",
      "65D30",
      "86A15"
    ],
    "keywords": [
      "random variable",
      "euclidean distance",
      "exact computation",
      "polyhedron",
      "cumulative distribution function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.0005G"
    }
  }
}