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:
- datanumpy:array_like, ndim=1
observed (one-dimensional) data
- return_binsbool, optional
if True, then return the bin edges
- Returns:
- width
python:float
optimal bin width using the Freedman-Diaconis rule
- bins
ndarray
bin edges: returned if
return_bins
is True
- width
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