scott_bin_width

astropy.stats.scott_bin_width(data: ArrayLike, return_bins: bool | None = False) → float | tuple[float, NDArray]

Return the optimal histogram bin width using Scott’s rule.

Scott’s rule is a normal reference rule: it minimizes the integrated mean squared error in the bin approximation under the assumption that the data is approximately Gaussian.

Parameters:

datanumpy:array_like, ndim=1

observed (one-dimensional) data

return_binsbool, optional

if True, then return the bin edges

Returns:

widthpython:float

optimal bin width using Scott’s rule

binsndarray

bin edges: returned if return_bins is True

See also

knuth_bin_width

freedman_bin_width

bayesian_blocks

histogram

Notes

The optimal bin width is

\[\Delta_b = \frac{3.5\sigma}{n^{1/3}}\]

where \(\sigma\) is the standard deviation of the data, and \(n\) is the number of data points [1].

References

[1]

Scott, David W. (1979). “On optimal and data-based histograms”. Biometricka 66 (3): 605-610