Help on function histogram in module numpy.lib.function_base:
histogram(a, bins=10, range=None, normed=False, weights=None, density=None)
Compute the histogram of a set of data.
Parameters
----------
a : array_like
Input data. The histogram is computed over the flattened array.
bins : int or sequence of scalars or str, optional
If `bins` is an int, it defines the number of equal-width
bins in the given range (10, by default). If `bins` is a
sequence, it defines the bin edges, including the rightmost
edge, allowing for non-uniform bin widths.
.. versionadded:: 1.11.0
If `bins` is a string from the list below, `histogram` will use
the method chosen to calculate the optimal bin width and
consequently the number of bins (see `Notes` for more detail on
the estimators) from the data that falls within the requested
range. While the bin width will be optimal for the actual data
in the range, the number of bins will be computed to fill the
entire range, including the empty portions. For visualisation,
using the 'auto' option is suggested. Weighted data is not
supported for automated bin size selection.
'auto'
Maximum of the 'sturges' and 'fd' estimators. Provides good
all round performance
'fd' (Freedman Diaconis Estimator)
Robust (resilient to outliers) estimator that takes into
account data variability and data size .
'doane'
An improved version of Sturges' estimator that works better
with non-normal datasets.
'scott'
Less robust estimator that that takes into account data
variability and data size.
'rice'
Estimator does not take variability into account, only data
size. Commonly overestimates number of bins required.
'sturges'
R's default method, only accounts for data size. Only
optimal for gaussian data and underestimates number of bins
for large non-gaussian datasets.
'sqrt'
Square root (of data size) estimator, used by Excel and
other programs for its speed and simplicity.
range : (float, float), optional
The lower and upper range of the bins. If not provided, range
is simply ``(a.min(), a.max())``. Values outside the range are
ignored. The first element of the range must be less than or
equal to the second. `range` affects the automatic bin
computation as well. While bin width is computed to be optimal
based on the actual data within `range`, the bin count will fill
the entire range including portions containing no data.
normed : bool, optional
This keyword is deprecated in Numpy 1.6 due to confusing/buggy
behavior. It will be removed in Numpy 2.0. Use the ``density``
keyword instead. If ``False``, the result will contain the
number of samples in each bin. If ``True``, the result is the
value of the probability *density* function at the bin,
normalized such that the *integral* over the range is 1. Note
that this latter behavior is known to be buggy with unequal bin
widths; use ``density`` instead.
weights : array_like, optional
An array of weights, of the same shape as `a`. Each value in
`a` only contributes its associated weight towards the bin count
(instead of 1). If `density` is True, the weights are
normalized, so that the integral of the density over the range
remains 1.
density : bool, optional
If ``False``, the result will contain the number of samples in
each bin. If ``True``, the result is the value of the
probability *density* function at the bin, normalized such that
the *integral* over the range is 1. Note that the sum of the
histogram values will not be equal to 1 unless bins of unity
width are chosen; it is not a probability *mass* function.
Overrides the ``normed`` keyword if given.
Returns
-------
hist : array
The values of the histogram. See `density` and `weights` for a
description of the possible semantics.
bin_edges : array of dtype float
Return the bin edges ``(length(hist)+1)``.
See Also
--------
histogramdd, bincount, searchsorted, digitize
Notes
-----
All but the last (righthand-most) bin is half-open. In other words,
if `bins` is::
[1, 2, 3, 4]
then the first bin is ``[1, 2)`` (including 1, but excluding 2) and
the second ``[2, 3)``. The last bin, however, is ``[3, 4]``, which
*includes* 4.
.. versionadded:: 1.11.0
The methods to estimate the optimal number of bins are well founded
in literature, and are inspired by the choices R provides for
histogram visualisation. Note that having the number of bins
proportional to :math:`n^{1/3}` is asymptotically optimal, which is
why it appears in most estimators. These are simply plug-in methods
that give good starting points for number of bins. In the equations
below, :math:`h` is the binwidth and :math:`n_h` is the number of
bins. All estimators that compute bin counts are recast to bin width
using the `ptp` of the data. The final bin count is obtained from
``np.round(np.ceil(range / h))`.
'Auto' (maximum of the 'Sturges' and 'FD' estimators)
A compromise to get a good value. For small datasets the Sturges
value will usually be chosen, while larger datasets will usually
default to FD. Avoids the overly conservative behaviour of FD
and Sturges for small and large datasets respectively.
Switchover point is usually :math:`a.size \approx 1000`.
'FD' (Freedman Diaconis Estimator)
.. math:: 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 too
conservative for small datasets, but is quite good for large
datasets. The IQR is very robust to outliers.
'Scott'
.. math:: h = \sigma \sqrt[3]{\frac{24 * \sqrt{\pi}}{n}}
The binwidth is proportional to the standard deviation of the
data and inversely proportional to cube root of ``x.size``. Can
be too conservative for small datasets, but is quite good for
large datasets. The standard deviation is not very robust to
outliers. Values are very similar to the Freedman-Diaconis
estimator in the absence of outliers.
'Rice'
.. math:: n_h = 2n^{1/3}
The number of bins is only proportional to cube root of
``a.size``. It tends to overestimate the number of bins and it
does not take into account data variability.
'Sturges'
.. math:: n_h = \log _{2}n+1
The number of bins is the base 2 log of ``a.size``. This
estimator assumes normality of data and is too conservative for
larger, non-normal datasets. This is the default method in R's
``hist`` method.
'Doane'
.. math:: 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 better
estimates for non-normal datasets. This estimator attempts to
account for the skew of the data.
'Sqrt'
.. math:: n_h = \sqrt n
The simplest and fastest estimator. Only takes into account the
data size.
Examples
--------
>>> np.histogram([1, 2, 1], bins=[0, 1, 2, 3])
(array([0, 2, 1]), array([0, 1, 2, 3]))
>>> np.histogram(np.arange(4), bins=np.arange(5), density=True)
(array([ 0.25, 0.25, 0.25, 0.25]), array([0, 1, 2, 3, 4]))
>>> np.histogram([[1, 2, 1], [1, 0, 1]], bins=[0,1,2,3])
(array([1, 4, 1]), array([0, 1, 2, 3]))
>>> a = np.arange(5)
>>> hist, bin_edges = np.histogram(a, density=True)
>>> hist
array([ 0.5, 0. , 0.5, 0. , 0. , 0.5, 0. , 0.5, 0. , 0.5])
>>> hist.sum()
2.4999999999999996
>>> np.sum(hist*np.diff(bin_edges))
1.0
.. versionadded:: 1.11.0
Automated Bin Selection Methods example, using 2 peak random data
with 2000 points:
>>> import matplotlib.pyplot as plt
>>> rng = np.random.RandomState(10) # deterministic random data
>>> a = np.hstack((rng.normal(size=1000),
... rng.normal(loc=5, scale=2, size=1000)))
>>> plt.hist(a, bins='auto') # plt.hist passes it's arguments to np.histogram
>>> plt.title("Histogram with 'auto' bins")
>>> plt.show()