{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The trapezoidal distribution can be represented with an up-sloping line from "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "loc"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " to "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "(loc + c*scale)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", then constant to "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "(loc + d*scale)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and then downsloping from "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "(loc + d*scale)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " to "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "(loc+scale)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ".  This defines the trapezoid base from "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "loc"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " to "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "(loc+scale)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and the flat top from "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "c"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " to "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "d"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " proportional to the position along the base with "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "0 <= c <= d <= 1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ".  When "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "c=d"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", this is equivalent to "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "triang",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.signal.windows._windows:triang"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " with the same values for "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "loc",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "scale",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.stats._qmc:scale"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "c",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". The method of "
            },
            {
              "__type": "FootnoteReference",
              "__tag": 4066,
              "label": "1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is used for computing moments."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "trapezoid",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.integrate._quadrature:trapezoid"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " takes "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "c"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "d"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " as shape parameters."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "%(after_notes)s"
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The standard form is in the range [0, 1] with c the mode. The location parameter shifts the start to "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "loc",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". The scale parameter changes the width from 1 to "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "scale",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.stats._qmc:scale"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "%(example)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 trapezoidal 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": 9909,
  "item_type": "class",
  "aliases": [
    "scipy.stats._continuous_distns.trapezoid_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": "trapezoid_gen"
  },
  "references": [
    ".. [1] Kacker, R.N. and Lawrence, J.F. (2007). Trapezoidal and triangular",
    "   distributions for Type B evaluation of standard uncertainty.",
    "   Metrologia 44, 117-127. :doi:`10.1088/0026-1394/44/2/003`"
  ],
  "qa": "scipy.stats._continuous_distns:trapezoid_gen",
  "arbitrary": [],
  "local_refs": []
}