{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The probability density function for "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "crystalball",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is:"
            }
          ]
        },
        {
          "__type": "Math",
          "__tag": 4058,
          "value": "f(x, \\beta, m) =  \\begin{cases}\n                    N \\exp(-x^2 / 2),  &\\text{for } x > -\\beta\\\\\n                    N A (B - x)^{-m}  &\\text{for } x \\le -\\beta\n                  \\end{cases}"
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "where "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "A = (m / |\\beta|)^m  \\exp(-\\beta^2 / 2)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "B = m/|\\beta| - |\\beta|"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "N"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is a normalisation constant."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "crystalball",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " takes "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "\\beta > 0"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "m > 1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " as shape parameters.  "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "\\beta"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " defines the point where the pdf changes from a power-law to a Gaussian distribution.  "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "m"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is the power of the power-law tail."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "%(after_notes)s"
            }
          ]
        },
        {
          "__type": "Admonition",
          "__tag": 4056,
          "kind": "versionadded",
          "base_type": "neutral",
          "children": [
            {
              "__type": "AdmonitionTitle",
              "__tag": 4055,
              "children": [
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": "versionadded 0.19.0"
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Yields": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Methods": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Returns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Crystalball distribution"
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Receives": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warnings": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Attributes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "%(before_notes)s"
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Other Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    }
  },
  "_ordered_sections": [
    "Summary",
    "Extended Summary",
    "Parameters",
    "Attributes",
    "Methods",
    "Returns",
    "Yields",
    "Receives",
    "Other Parameters",
    "Raises",
    "Warns",
    "Warnings",
    "Notes"
  ],
  "item_file": "/scipy/stats/_continuous_distns.py",
  "item_line": 11618,
  "item_type": "class",
  "aliases": [
    "scipy.stats._continuous_distns.crystalball_gen"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "momtype",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "1"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "a",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "b",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "xtol",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "1e-14"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "badvalue",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "name",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "longname",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "shapes",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "seed",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "None"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "crystalball_gen"
  },
  "references": [
    ".. [1] \"Crystal Ball Function\",",
    "       https://en.wikipedia.org/wiki/Crystal_Ball_function",
    "",
    "%(example)s"
  ],
  "qa": "scipy.stats._continuous_distns:crystalball_gen",
  "arbitrary": [],
  "local_refs": []
}