# scipy.stats.skew

scipy.stats.skew(a, axis=0, bias=True, nan_policy='propagate')

  Compute the sample skewness of a data set.

  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, optional

      Axis along which skewness is calculated. Default is 0. If None, compute over the whole array a.

    bias bool, optional

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

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

      Defines how to handle when input contains nan. The following options are available (default is ‘propagate’):

      > - ‘propagate’: returns nan

      > - ‘raise’: throws an error

      > - ‘omit’: performs the calculations ignoring nan values

  Returns
    skewness ndarray

      The skewness of values along an axis, returning 0 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

  \[m_i=\frac{1}{N}\sum_{n=1}^N(x[n]-\bar{x})^i\]

  is the biased sample \(i\texttt{th}\) central moment, and \(\bar{x}\) 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.

  \[G_1=\frac{k_3}{k_2^{3/2}}= \frac{\sqrt{N(N-1)}}{N-2}\frac{m_3}{m_2^{3/2}}.\]

  References

  1

    Zwillinger, D. and Kokoska, S. (2000). CRC Standard Probability and Statistics Tables and Formulae. Chapman & Hall: New York. 2000. Section 2.2.24.1

  Examples

      >>> from scipy.stats import skew
      >>> skew([1, 2, 3, 4, 5])
      0.0
      >>> skew([2, 8, 0, 4, 1, 9, 9, 0])
      0.2650554122698573

scipy.stats.moment scipy.stats.kstat