{
  "id": "2312.02965",
  "version": "v1",
  "published": "2023-12-05T18:53:42.000Z",
  "updated": "2023-12-05T18:53:42.000Z",
  "title": "Conditional constrained and unconstrained quantization for probability distributions",
  "authors": [
    "Megha Pandey",
    "Mrinal Kanti Roychowdhury"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article, we present the idea of conditional quantization for a Borel probability measure $P$ on a normed space $\\mathbb R^k$. We introduce the concept of conditional quantization in both constrained and unconstrained scenarios, along with defining the conditional quantization errors, dimensions, and coefficients in each case. We then calculate these values for specific probability distributions. Additionally, we demonstrate that for a Borel probability measure, the lower and upper quantization dimensions and coefficients do not depend on the conditional set of the conditional quantization in both constrained and unconstrained quantization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-05T18:53:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60Exx",
      "94A34"
    ],
    "keywords": [
      "unconstrained quantization",
      "borel probability measure",
      "conditional quantization errors",
      "specific probability distributions",
      "upper quantization dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}