{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "The k-th moment of a data sample is:"
            }
          ]
        },
        {
          "__type": "Math",
          "__tag": 4058,
          "value": "m_k = \\frac{1}{n} \\sum_{i = 1}^n (x_i - c)^k"
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Where "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "n",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is the number of samples, and "
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "c",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is the center around which the moment is calculated. This function uses exponentiation by squares "
            },
            {
              "__type": "FootnoteReference",
              "__tag": 4066,
              "label": "1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " for efficiency."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Note that, if "
            },
            {
              "__type": "ParamRef",
              "__tag": 4071,
              "name": "a"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is an empty array ("
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "a.size == 0"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "), array "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "moment",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.stats._stats_py:moment"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " with one element ("
            },
            {
              "__type": "InlineRole",
              "__tag": 4003,
              "value": "moment.size == 1",
              "domain": null,
              "role": null,
              "inventory": null
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ") is treated the same as scalar "
            },
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "moment",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.stats._stats_py:moment"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " ("
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "np.isscalar(moment)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "). This might produce arrays of unexpected shape."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Beginning in SciPy 1.9, "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "np.matrix"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " inputs (not recommended for new code) are converted to "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "np.ndarray"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " before the calculation is performed. In this case, the output will be a scalar or "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "np.ndarray"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " of appropriate shape rather than a 2D "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "np.matrix"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "np.ndarray"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " rather than a masked array with "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "mask=False"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "."
            }
          ]
        }
      ],
      "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": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "n-th moment about the `center`",
              "annotation": "ndarray or float",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The appropriate moment along the given axis or over all values if axis is None. The denominator for the moment calculation is the number of observations, no degrees of freedom correction is done."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Calculate the nth moment about the mean for a sample."
            }
          ]
        }
      ],
      "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": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "a",
              "annotation": "array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Input array."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "order",
              "annotation": "int or 1-D array_like of ints, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Order of central moment that is returned. Default is 1."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "axis",
              "annotation": "int or None, default: 0",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "None"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", the input will be raveled before computing the statistic."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "nan_policy",
              "annotation": "{'propagate', 'omit', 'raise'}",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Defines how to handle input NaNs."
                    }
                  ]
                },
                {
                  "__type": "BulletList",
                  "__tag": 4053,
                  "ordered": false,
                  "start": 1,
                  "children": [
                    {
                      "__type": "ListItem",
                      "__tag": 4054,
                      "children": [
                        {
                          "__type": "Paragraph",
                          "__tag": 4045,
                          "children": [
                            {
                              "__type": "InlineCode",
                              "__tag": 4051,
                              "value": "propagate"
                            },
                            {
                              "__type": "Text",
                              "__tag": 4046,
                              "value": ": if a NaN is present in the axis slice (e.g. row) along   which the  statistic is computed, the corresponding entry of the output   will be NaN."
                            }
                          ]
                        }
                      ]
                    },
                    {
                      "__type": "ListItem",
                      "__tag": 4054,
                      "children": [
                        {
                          "__type": "Paragraph",
                          "__tag": 4045,
                          "children": [
                            {
                              "__type": "InlineCode",
                              "__tag": 4051,
                              "value": "omit"
                            },
                            {
                              "__type": "Text",
                              "__tag": 4046,
                              "value": ": NaNs will be omitted when performing the calculation.   If insufficient data remains in the axis slice along which the   statistic is computed, the corresponding entry of the output will be   NaN."
                            }
                          ]
                        }
                      ]
                    },
                    {
                      "__type": "ListItem",
                      "__tag": 4054,
                      "children": [
                        {
                          "__type": "Paragraph",
                          "__tag": 4045,
                          "children": [
                            {
                              "__type": "InlineCode",
                              "__tag": 4051,
                              "value": "raise"
                            },
                            {
                              "__type": "Text",
                              "__tag": 4046,
                              "value": ": if a NaN is present, a "
                            },
                            {
                              "__type": "InlineCode",
                              "__tag": 4051,
                              "value": "ValueError"
                            },
                            {
                              "__type": "Text",
                              "__tag": 4046,
                              "value": " will be raised."
                            }
                          ]
                        }
                      ]
                    }
                  ]
                },
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "nan_policy='raise'"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " and "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "nan_policy='omit'"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " are not supported by lazy backends, and "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "nan_policy='omit'"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is not compatible with MArray input. For multidimensional input, "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "nan_policy='omit'"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is supported only by the NumPy backend. Instead, mask NaN values using "
                    },
                    {
                      "__type": "Link",
                      "__tag": 4049,
                      "children": [
                        {
                          "__type": "Text",
                          "__tag": 4046,
                          "value": "MArray"
                        }
                      ],
                      "url": "https://mdhaber.github.io/marray/tutorial.html",
                      "title": ""
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "; and use the default "
                    },
                    {
                      "__type": "ParamRef",
                      "__tag": 4071,
                      "name": "nan_policy"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ". See Notes for support information."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "center",
              "annotation": "float or None, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The point about which moments are taken. This can be the sample mean, the origin, or any other be point. If "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "None",
                      "reference": {
                        "__type": "RefInfo",
                        "__tag": 4000,
                        "module": "builtins",
                        "version": "?",
                        "kind": "module",
                        "path": "builtins:None"
                      },
                      "kind": "module"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " (default) compute the center as the sample mean."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "keepdims",
              "annotation": "bool, default: False",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "A moment is a specific quantitative measure of the shape of a set of points. It is often used to calculate coefficients of skewness and kurtosis due to its close relationship with them."
            }
          ]
        }
      ],
      "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": "build-install/usr/lib/python3.14/site-packages/scipy/stats/_stats_py.py",
  "item_line": 1084,
  "item_type": "function",
  "aliases": [
    "scipy.stats.moment"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "from scipy.stats import moment\n",
        "execution_status": "success",
        "out": ""
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "moment([1, 2, 3, 4, 5], order=1)\nmoment([1, 2, 3, 4, 5], order=2)\n",
        "execution_status": "failure",
        "out": "np.float64(2.0)\n"
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "describe",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.stats._stats_py:describe"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": "func"
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "kurtosis",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.stats._stats_py:kurtosis"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": "func"
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "skew",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "scipy.stats._stats_py:skew"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": "func"
    }
  ],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "a",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "order",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "1"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "axis",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "0"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "nan_policy",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": "propagate"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "center",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "KEYWORD_ONLY",
        "default": "None"
      },
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "keepdims",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "KEYWORD_ONLY",
        "default": "False"
      }
    ],
    "return_annotation": {
      "__type": "Empty",
      "__tag": 4031
    },
    "target_name": "moment"
  },
  "references": [
    ".. [1] https://eli.thegreenplace.net/2009/03/21/efficient-integer-exponentiation-algorithms"
  ],
  "qa": "scipy.stats._stats_py:moment",
  "arbitrary": [],
  "local_refs": [
    "a",
    "axis",
    "center",
    "keepdims",
    "n-th moment about the `center`",
    "nan_policy",
    "order"
  ]
}