{
  "id": "2406.02894",
  "version": "v1",
  "published": "2024-06-05T03:28:07.000Z",
  "updated": "2024-06-05T03:28:07.000Z",
  "title": "The Bunching and Monotonicity Properties of Families of Probability Distributions",
  "authors": [
    "S. Portnoy",
    "N. Torrado",
    "J. J. P. Veerman"
  ],
  "comment": "19 pages, 4 figures",
  "categories": [
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of stochastic order by concentration. We give an application to the Beta family of distributions, and specifically to the one-parameter subfamily with constant mean. This leads to using U.S. household income data to fit generalized Beta distributions and offers a new measure of income concentration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-05T03:28:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "62E99"
    ],
    "keywords": [
      "probability distributions",
      "monotonicity properties",
      "fit generalized beta distributions",
      "household income data",
      "fundamental concept"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}