{
  "id": "2312.16615",
  "version": "v1",
  "published": "2023-12-27T15:47:18.000Z",
  "updated": "2023-12-27T15:47:18.000Z",
  "title": "Constrained quantization for a uniform distribution",
  "authors": [
    "Pigar Biteng",
    "Mathieu Caguiat",
    "Dipok Deb",
    "Mrinal Kanti Roychowdhury",
    "Beatriz Vela Villanueva"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points lying on a specific set. The specific set is known as the constraint of the constrained quantization. A quantization without a constraint is known as an unconstrained quantization, which traditionally in the literature is known as quantization. Constrained quantization has recently been introduced by Pandey and Roychowdhury. In this paper, for a uniform distribution with support lying on a side of an equilateral triangle, and the constraint as the union of the other two sides, we obtain the optimal sets of $n$-points and the $n$th constrained quantization errors for all positive integers $n$. We also calculate the constrained quantization dimension and the constrained quantization coefficient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-27T15:47:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60Exx",
      "94A34"
    ],
    "keywords": [
      "uniform distribution",
      "specific set",
      "borel probability measure refers",
      "constraint",
      "th constrained quantization errors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}