{
  "id": "1307.3433",
  "version": "v1",
  "published": "2013-07-12T12:23:56.000Z",
  "updated": "2013-07-12T12:23:56.000Z",
  "title": "Approximating Mills ratio",
  "authors": [
    "Armengol Gasull",
    "Frederic Utzet"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider the Mills ratio $f(x)=\\big(1-\\Phi(x)\\big)/\\phi(x), \\, x\\ge 0$, where $\\phi$ is the density function of the standard Gaussian law and $\\Phi$ its cumulative distribution.We introduce a general procedure to approximate $f$ on the whole $[0,\\infty)$ which allows to prove interesting properties where $f$ is involved. As applications we present a new proof that $1/f$ is strictly convex, and we give new sharp bounds of $f$ involving rational functions, functions with square roots or exponential terms. Also Chernoff type bounds for the Gaussian $Q$--function are studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-12T12:23:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "approximating mills ratio",
      "chernoff type bounds",
      "standard gaussian law",
      "density function",
      "exponential terms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.3433G"
    }
  }
}