{
  "id": "2012.13578",
  "version": "v1",
  "published": "2020-12-25T14:07:53.000Z",
  "updated": "2020-12-25T14:07:53.000Z",
  "title": "Monotonicity properties of the gamma family of distributions",
  "authors": [
    "Iosif Pinelis"
  ],
  "comment": "To appear in Statistics and Probability Letters",
  "categories": [
    "math.PR",
    "math.CA"
  ],
  "abstract": "For real $a>0$, let $X_a$ denote a random variable with the gamma distribution with parameters $a$ and $1$. Then $\\mathsf P(X_a-a>c)$ is increasing in $a$ for each real $c\\ge0$; non-increasing in $a$ for each real $c\\le-1/3$; and non-monotonic in $a$ for each $c\\in(-1/3,0)$. This extends and/or refines certain previously established results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-25T14:07:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D15",
      "33B20",
      "60E15",
      "62E15"
    ],
    "keywords": [
      "monotonicity properties",
      "gamma family",
      "gamma distribution",
      "parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}