`scipy.stats._stats_py:skew`

source: /scipy/stats/_stats_py.py :1255

Signature

   def     skew (    a    ,    axis    =  0   ,    bias    =  True   ,    nan_policy    =  propagate   ,  * ,     keepdims    =  False     )

Summary

Compute the sample skewness of a data set.

Extended Summary

For normally distributed data, the skewness should be about zero. For unimodal continuous distributions, a skewness value greater than zero means that there is more weight in the right tail of the distribution. The function skewtest can be used to determine if the skewness value is close enough to zero, statistically speaking.

Parameters

a : ndarray

Input array.

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.

bias : bool, optional

If False, then the calculations are corrected for statistical bias.

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.

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

skewness : ndarray: The skewness of values along an axis, returning NaN where all values are equal.

Notes

The sample skewness is computed as the Fisher-Pearson coefficient of skewness, i.e.

g_{1} = \frac{m _{3}}{m _{2}^{3/2}}

where

m_{i} = \frac{1}{N} n = 1 \sum N (x [n] - \overset{x}{ˉ})^{i}

is the biased sample $i th$ central moment, and $\overset{x}{ˉ}$ is the sample mean. If bias is False, the calculations are corrected for bias and the value computed is the adjusted Fisher-Pearson standardized moment coefficient, i.e.

G_{1} = \frac{k _{3}}{k _{2}^{3/2}} = \frac{N ( N - 1 )}{N - 2} \frac{m _{3}}{m _{2}^{3/2}} .

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.

Array API Standard Support

skew has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ✅                   
JAX                   ⚠️ no JIT             ⚠️ no JIT           
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

from scipy.stats import skew

✓

skew([1, 2, 3, 4, 5])
skew([2, 8, 0, 4, 1, 9, 9, 0])