{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "WCSZYPBZY4"
    },
    {
      "field": "uses",
      "target": "XE3913G5SA"
    },
    {
      "field": "defines",
      "target": "ZGYA090JP2"
    }
  ],
  "body": "\n## Summary\n\nThe complementary error function is $\\operatorname{erfc} x = 1 - \\operatorname{erf} x$, where $\\operatorname{erf}$ is the [[error function|7Y56QCZSZJ]].\nIt equals $\\frac{2}{\\sqrt{\\pi}} \\int_x^\\infty e^{-t^2}\\, dt$, the scaled area of the tail of the Gaussian curve.\nIt is the natural function for small tail probabilities of the [[normal distribution|05AQE0QR0D]], where computing $1 - \\operatorname{erf} x$ directly would lose precision.\n\n## Explanations\n\n### L1 human\n\nThe error function measures the area under the bell curve from $0$ up to $x$.\nThe complementary error function measures what is left: the area beyond $x$.\nIt starts at $1$ for $x = 0$ and drops very fast to $0$ as $x$ grows.\nFor example, $\\operatorname{erfc} 3 \\approx 2.2 \\times 10^{-5}$, a tiny tail.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "33B20"
    ],
    "name": "Complementary error function",
    "sources": [
      {
        "locator": "Complementary error function",
        "url": "https://en.wikipedia.org/wiki/Error_function"
      }
    ],
    "tag": "TZ3CT1YA9B"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/TZ3CT1YA9B/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/TZ3CT1YA9B.md",
  "msc": [
    "33B20"
  ],
  "name": "Complementary error function",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/TZ3/TZ3CT1YA9B.md",
  "status": null,
  "tag": "TZ3CT1YA9B",
  "uri": "m2://TZ3CT1YA9B",
  "url": "https://tamnd.github.io/math2/wiki/complementary-error-function/",
  "writing": {
    "tag": "TZ3CT1YA9B",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}