freedman_bin_width

astropy.stats.freedman_bin_width(data, return_bins=False)

Return the optimal histogram bin width using the Freedman-Diaconis rule.

The Freedman-Diaconis rule is a normal reference rule like Scott’s rule, but uses rank-based statistics for results which are more robust to deviations from a normal distribution.

Parameters:

dataarray_like, ndim=1

observed (one-dimensional) data

return_binsbool, optional

if True, then return the bin edges

Returns:

widthfloat

optimal bin width using the Freedman-Diaconis rule

binsndarray

bin edges: returned if return_bins is True

See also

knuth_bin_width

scott_bin_width

bayesian_blocks

histogram

Notes

The optimal bin width is

\[\Delta_b = \frac{2(q_{75} - q_{25})}{n^{1/3}}\]

where \(q_{N}\) is the \(N\) percent quartile of the data, and \(n\) is the number of data points [1].

References

[1]

D. Freedman & P. Diaconis (1981) “On the histogram as a density estimator: L2 theory”. Probability Theory and Related Fields 57 (4): 453-476