scipy.stats.moment

scipy.stats.moment(a, moment=1, axis=0, nan_policy='propagate', *, 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

aarray_like

Input array.

momentint or array_like of ints, optional

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

axisint 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.

keepdimsbool, 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 central momentndarray 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 central moment of a data sample is:

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

Where n is the number of samples and x-bar is the mean. 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