polars.Expr.skew

Expr.skew(*, bias: bool = True) → Self

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.

See scipy.stats for more information.

Parameters:

biasbool, optional

If False, the calculations are corrected for statistical bias.

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.

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

Examples

>>> df = pl.DataFrame({"a": [1, 2, 3, 2, 1]})
>>> df.select(pl.col("a").skew())
shape: (1, 1)
┌──────────┐
│ a        │
│ ---      │
│ f64      │
╞══════════╡
│ 0.343622 │
└──────────┘