# freedman_bin_width¶

astropy.stats.freedman_bin_width(data, return_bins=False)[source]

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

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