# scipy.stats.moment

scipy.stats.moment(a, moment=1, axis=0, nan_policy='propagate', *, center=None, keepdims=False)

  Calculate the nth moment about the mean for a sample.

  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.

  Parameters:
    a array_like

      Input array.

    moment int or array_like of ints, optional

      Order of central moment that is returned. Default is 1.

    axis int or None, default: 0

      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 `None`, the input will be raveled before computing the statistic.

    nan_policy{‘propagate’, ‘omit’, ‘raise’}

      Defines how to handle input NaNs.

      - `propagate`: 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.

      - `omit`: 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.

      - `raise`: if a NaN is present, a `ValueError` will be raised.

    center float or None, optional

      The point about which moments are taken. This can be the sample mean, the origin, or any other be point. If None (default) compute the center as the sample mean.

    keepdims bool, default: False

      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.

  Returns:
    n-th moment about the `center` ndarray or float

      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.

  See also

  `kurtosis`, `skew`, `describe`

  Notes

  The k-th moment of a data sample is:

  \[m_k = \frac{1}{n} \sum_{i = 1}^n (x_i - c)^k\]

  Where n is the number of samples, and c is the center around which the moment is calculated. This function uses exponentiation by squares [1] for efficiency.

  Note that, if a is an empty array (`a.size == 0`), array `moment` with one element (moment.size == 1) is treated the same as scalar `moment` (`np.isscalar(moment)`). This might produce arrays of unexpected shape.

  Beginning in SciPy 1.9, `np.matrix` inputs (not recommended for new code) are converted to `np.ndarray` before the calculation is performed. In this case, the output will be a scalar or `np.ndarray` of appropriate shape rather than a 2D `np.matrix`. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or `np.ndarray` rather than a masked array with `mask=False`.

  References

  [1]

  https://eli.thegreenplace.net/2009/03/21/efficient-integer-exponentiation-algorithms

  Examples

      >>> from scipy.stats import moment
      >>> moment([1, 2, 3, 4, 5], moment=1)
      0.0
      >>> moment([1, 2, 3, 4, 5], moment=2)
      2.0