{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {},
  "_ordered_sections": [],
  "item_file": null,
  "item_line": null,
  "item_type": null,
  "aliases": [],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [],
  "signature": null,
  "references": null,
  "qa": "tutorial:stats:continuous_vonmises",
  "arbitrary": [
    {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "There is one shape parameter "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "\\kappa>0"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", with support "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "x\\in\\left[-\\pi,\\pi\\right]"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". For values of "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "\\kappa<100"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " the PDF and CDF formulas below are used. Otherwise, a normal approximation with variance "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "1/\\kappa"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is used. [Note that the PDF and CDF functions below are periodic with period "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "2\\pi"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". If an input outside "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "x\\in\\left[-\\pi,\\pi\\right]"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is given, it is converted to the equivalent angle in this range.]"
            }
          ]
        },
        {
          "__type": "Math",
          "__tag": 4058,
          "value": ""
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "where  "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "I_{k}(\\kappa)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is a modified Bessel function of the first kind."
            }
          ]
        },
        {
          "__type": "Math",
          "__tag": 4058,
          "value": ""
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "This can be used for defining circular variance."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Implementation: "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "scipy.stats.vonmises",
              "domain": null,
              "role": null,
              "inventory": null
            }
          ]
        }
      ],
      "title": [
        {
          "__type": "Text",
          "__tag": 4046,
          "value": "Von Mises Distribution"
        }
      ],
      "level": 0,
      "target": "continuous-vonmises"
    }
  ],
  "local_refs": []
}