knuth_bin_width¶
-
astropy.stats.
knuth_bin_width
(data, return_bins=False, quiet=True)[source] [edit on github]¶ Return the optimal histogram bin width using Knuth’s rule.
Knuth’s rule is a fixed-width, Bayesian approach to determining the optimal bin width of a histogram.
Parameters: - data : array-like, ndim=1
observed (one-dimensional) data
- return_bins : bool (optional)
if True, then return the bin edges
- quiet : bool (optional)
if True (default) then suppress stdout output from scipy.optimize
Returns: - dx : float
optimal bin width. Bins are measured starting at the first data point.
- bins : ndarray
bin edges: returned if
return_bins
is True
See also
freedman_bin_width
,scott_bin_width
,bayesian_blocks
,histogram
Notes
The optimal number of bins is the value M which maximizes the function
\[F(M|x,I) = n\log(M) + \log\Gamma(\frac{M}{2}) - M\log\Gamma(\frac{1}{2}) - \log\Gamma(\frac{2n+M}{2}) + \sum_{k=1}^M \log\Gamma(n_k + \frac{1}{2})\]where \(\Gamma\) is the Gamma function, \(n\) is the number of data points, \(n_k\) is the number of measurements in bin \(k\) [1].
References
[1] (1, 2) Knuth, K.H. “Optimal Data-Based Binning for Histograms”. arXiv:0605197, 2006