numpy.histogram_bin_edges¶

numpy.histogram_bin_edges(a,bins=10,range=None,weights=None)[source]¶

Function to calculate only the edges of the bins used by thehistogram function.

Parameters:

a:array_like Input data. The histogram is computed over the flattened array. bins:int or sequence of scalars or str, optional Ifbins is an int, it defines the number of equal-widthbins in the given range (10, by default). Ifbins is asequence, it defines the bin edges, including the rightmostedge, allowing for non-uniform bin widths. Ifbins is a string from the list below,histogram_bin_edges will usethe method chosen to calculate the optimal bin width andconsequently the number of bins (seeNotes for more detail onthe estimators) from the data that falls within the requestedrange. While the bin width will be optimal for the actual datain the range, the number of bins will be computed to fill theentire range, including the empty portions. For visualisation,using the ‘auto’ option is suggested. Weighted data is notsupported for automated bin size selection. ‘auto’ Maximum of the ‘sturges’ and ‘fd’ estimators. Provides goodall around performance. ‘fd’ (Freedman Diaconis Estimator) Robust (resilient to outliers) estimator that takes intoaccount data variability and data size. ‘doane’ An improved version of Sturges’ estimator that works betterwith non-normal datasets. ‘scott’ Less robust estimator that that takes into account datavariability and data size. ‘rice’ Estimator does not take variability into account, only datasize. Commonly overestimates number of bins required. ‘sturges’ R’s default method, only accounts for data size. Onlyoptimal for gaussian data and underestimates number of binsfor large non-gaussian datasets. ‘sqrt’ Square root (of data size) estimator, used by Excel andother programs for its speed and simplicity. range:(float, float), optional The lower and upper range of the bins. If not provided, rangeis simply(a.min(),a.max()). Values outside the range areignored. The first element of the range must be less than orequal to the second.range affects the automatic bincomputation as well. While bin width is computed to be optimalbased on the actual data withinrange, the bin count will fillthe entire range including portions containing no data. weights:array_like, optional An array of weights, of the same shape asa. Each value ina only contributes its associated weight towards the bin count(instead of 1). This is currently not used by any of the bin estimators,but may be in the future.

Returns:

bin_edges:array of dtype float The edges to pass intohistogram

See also

histogram

Notes

The methods to estimate the optimal number of bins are well foundedin literature, and are inspired by the choices R provides forhistogram visualisation. Note that having the number of binsproportional ton^{1/3} is asymptotically optimal, which iswhy it appears in most estimators. These are simply plug-in methodsthat give good starting points for number of bins. In the equationsbelow,h is the binwidth andn_h is the number ofbins. All estimators that compute bin counts are recast to bin widthusing theptp of the data. The final bin count is obtained fromnp.round(np.ceil(range/h)).

‘Auto’ (maximum of the ‘Sturges’ and ‘FD’ estimators)

A compromise to get a good value. For small datasets the Sturgesvalue will usually be chosen, while larger datasets will usuallydefault to FD. Avoids the overly conservative behaviour of FDand Sturges for small and large datasets respectively.Switchover point is usuallya.size \approx 1000.

‘FD’ (Freedman Diaconis Estimator)

h = 2 \frac{IQR}{n^{1/3}}

The binwidth is proportional to the interquartile range (IQR)and inversely proportional to cube root of a.size. Can be tooconservative for small datasets, but is quite good for largedatasets. The IQR is very robust to outliers.

‘Scott’

h = \sigma \sqrt[3]{\frac{24 * \sqrt{\pi}}{n}}

The binwidth is proportional to the standard deviation of thedata and inversely proportional to cube root ofx.size. Canbe too conservative for small datasets, but is quite good forlarge datasets. The standard deviation is not very robust tooutliers. Values are very similar to the Freedman-Diaconisestimator in the absence of outliers.

‘Rice’

n_h = 2n^{1/3}

The number of bins is only proportional to cube root ofa.size. It tends to overestimate the number of bins and itdoes not take into account data variability.

‘Sturges’

n_h = \log _{2}n+1

The number of bins is the base 2 log ofa.size. Thisestimator assumes normality of data and is too conservative forlarger, non-normal datasets. This is the default method in R’shist method.

‘Doane’

n_h = 1 + \log_{2}(n) + \log_{2}(1 + \frac{|g_1|}{\sigma_{g_1}})g_1 = mean[(\frac{x - \mu}{\sigma})^3]\sigma_{g_1} = \sqrt{\frac{6(n - 2)}{(n + 1)(n + 3)}}

An improved version of Sturges’ formula that produces betterestimates for non-normal datasets. This estimator attempts toaccount for the skew of the data.

‘Sqrt’

n_h = \sqrt n

The simplest and fastest estimator. Only takes into account thedata size.

Examples

>>>arr=np.array([0,0,0,1,2,3,3,4,5])>>>np.histogram_bin_edges(arr,bins='auto',range=(0,1))array([0.  , 0.25, 0.5 , 0.75, 1.  ])>>>np.histogram_bin_edges(arr,bins=2)array([0. , 2.5, 5. ])

For consistency with histogram, an array of pre-computed bins ispassed through unmodified:

>>>np.histogram_bin_edges(arr,[1,2])array([1, 2])

This function allows one set of bins to be computed, and reused acrossmultiple histograms:

>>>shared_bins=np.histogram_bin_edges(arr,bins='auto')>>>shared_binsarray([0., 1., 2., 3., 4., 5.])

>>>group_id=np.array([0,1,1,0,1,1,0,1,1])>>>hist_0,_=np.histogram(arr[group_id==0],bins=shared_bins)>>>hist_1,_=np.histogram(arr[group_id==1],bins=shared_bins)

>>>hist_0;hist_1array([1, 1, 0, 1, 0])array([2, 0, 1, 1, 2])

Which gives more easily comparable results than using separate bins foreach histogram:

>>>hist_0,bins_0=np.histogram(arr[group_id==0],bins='auto')>>>hist_1,bins_1=np.histogram(arr[group_id==1],bins='auto')>>>hist_0;hist1array([1, 1, 1])array([2, 1, 1, 2])>>>bins_0;bins_1array([0., 1., 2., 3.])array([0.  , 1.25, 2.5 , 3.75, 5.  ])