{
  "__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": "betaprime",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is:"
            }
          ]
        },
        {
          "__type": "Math",
          "__tag": 4058,
          "value": "f(x, a, b) = \\frac{x^{a-1} (1+x)^{-a-b}}{\\beta(a, b)}"
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "for "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "x >= 0"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "a > 0"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "b > 0"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", where "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "\\beta(a, b)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is the beta function (see "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "scipy.special.beta",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ")."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "betaprime",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " takes "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "b"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " as shape parameters."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The distribution is related to the "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "beta",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.special.cython_special:beta"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " distribution as follows: If "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "X"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " follows a beta distribution with parameters "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "a, b"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", then "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "Y = X/(1-X)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " has a beta prime distribution with parameters "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "a, b"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " ("
            },
            {
              "__type": "FootnoteReference",
              "__tag": 4066,
              "label": "1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ")."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The beta prime distribution is a reparametrized version of the F distribution.  The beta prime distribution with shape parameters "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "b"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "scale = s"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is equivalent to the F distribution with parameters "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "d1 = 2*a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "d2 = 2*b"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "scale = (a/b)*s"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". For example,"
            }
          ]
        },
        {
          "__type": "Code",
          "__tag": 4050,
          "value": ">>> from scipy.stats import betaprime, f\n>>> x = [1, 2, 5, 10]\n>>> a = 12\n>>> b = 5\n>>> betaprime.pdf(x, a, b, scale=2)\narray([0.00541179, 0.08331299, 0.14669185, 0.03150079])\n>>> f.pdf(x, 2*a, 2*b, scale=(a/b)*2)\narray([0.00541179, 0.08331299, 0.14669185, 0.03150079])",
          "execution_status": null
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "%(after_notes)s"
            }
          ]
        }
      ],
      "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": "A beta prime continuous random variable."
            }
          ]
        }
      ],
      "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": 973,
  "item_type": "class",
  "aliases": [
    "scipy.stats._continuous_distns.betaprime_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": "betaprime_gen"
  },
  "references": [
    ".. [1] Beta prime distribution, Wikipedia,",
    "       https://en.wikipedia.org/wiki/Beta_prime_distribution",
    "",
    "%(example)s"
  ],
  "qa": "scipy.stats._continuous_distns:betaprime_gen",
  "arbitrary": [],
  "local_refs": []
}