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Module « scipy.stats »

Fonction binned_statistic - module scipy.stats

Signature de la fonction binned_statistic

def binned_statistic(x, values, statistic='mean', bins=10, range=None) 

Description

help(scipy.stats.binned_statistic)

Compute a binned statistic for one or more sets of data.

This is a generalization of a histogram function.  A histogram divides
the space into bins, and returns the count of the number of points in
each bin.  This function allows the computation of the sum, mean, median,
or other statistic of the values (or set of values) within each bin.

Parameters
----------
x : (N,) array_like
    A sequence of values to be binned.
values : (N,) array_like or list of (N,) array_like
    The data on which the statistic will be computed.  This must be
    the same shape as `x`, or a set of sequences - each the same shape as
    `x`.  If `values` is a set of sequences, the statistic will be computed
    on each independently.
statistic : string or callable, optional
    The statistic to compute (default is 'mean').
    The following statistics are available:

      * 'mean' : compute the mean of values for points within each bin.
        Empty bins will be represented by NaN.
      * 'std' : compute the standard deviation within each bin. This
        is implicitly calculated with ddof=0.
      * 'median' : compute the median of values for points within each
        bin. Empty bins will be represented by NaN.
      * 'count' : compute the count of points within each bin.  This is
        identical to an unweighted histogram.  `values` array is not
        referenced.
      * 'sum' : compute the sum of values for points within each bin.
        This is identical to a weighted histogram.
      * 'min' : compute the minimum of values for points within each bin.
        Empty bins will be represented by NaN.
      * 'max' : compute the maximum of values for point within each bin.
        Empty bins will be represented by NaN.
      * function : a user-defined function which takes a 1D array of
        values, and outputs a single numerical statistic. This function
        will be called on the values in each bin.  Empty bins will be
        represented by function([]), or NaN if this returns an error.

bins : int or sequence of scalars, 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.  Values in `x` that are smaller than lowest bin edge are
    assigned to bin number 0, values beyond the highest bin are assigned to
    ``bins[-1]``.  If the bin edges are specified, the number of bins will
    be, (nx = len(bins)-1).
range : (float, float) or [(float, float)], optional
    The lower and upper range of the bins.  If not provided, range
    is simply ``(x.min(), x.max())``.  Values outside the range are
    ignored.

Returns
-------
statistic : array
    The values of the selected statistic in each bin.
bin_edges : array of dtype float
    Return the bin edges ``(length(statistic)+1)``.
binnumber: 1-D ndarray of ints
    Indices of the bins (corresponding to `bin_edges`) in which each value
    of `x` belongs.  Same length as `values`.  A binnumber of `i` means the
    corresponding value is between (bin_edges[i-1], bin_edges[i]).

See Also
--------
numpy.digitize, numpy.histogram, binned_statistic_2d, binned_statistic_dd

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:: 0.11.0

Examples
--------
>>> import numpy as np
>>> from scipy import stats
>>> import matplotlib.pyplot as plt

First some basic examples:

Create two evenly spaced bins in the range of the given sample, and sum the
corresponding values in each of those bins:

>>> values = [1.0, 1.0, 2.0, 1.5, 3.0]
>>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2)
BinnedStatisticResult(statistic=array([4. , 4.5]),
        bin_edges=array([1., 4., 7.]), binnumber=array([1, 1, 1, 2, 2]))

Multiple arrays of values can also be passed.  The statistic is calculated
on each set independently:

>>> values = [[1.0, 1.0, 2.0, 1.5, 3.0], [2.0, 2.0, 4.0, 3.0, 6.0]]
>>> stats.binned_statistic([1, 1, 2, 5, 7], values, 'sum', bins=2)
BinnedStatisticResult(statistic=array([[4. , 4.5],
       [8. , 9. ]]), bin_edges=array([1., 4., 7.]),
       binnumber=array([1, 1, 1, 2, 2]))

>>> stats.binned_statistic([1, 2, 1, 2, 4], np.arange(5), statistic='mean',
...                        bins=3)
BinnedStatisticResult(statistic=array([1., 2., 4.]),
        bin_edges=array([1., 2., 3., 4.]),
        binnumber=array([1, 2, 1, 2, 3]))

As a second example, we now generate some random data of sailing boat speed
as a function of wind speed, and then determine how fast our boat is for
certain wind speeds:

>>> rng = np.random.default_rng()
>>> windspeed = 8 * rng.random(500)
>>> boatspeed = .3 * windspeed**.5 + .2 * rng.random(500)
>>> bin_means, bin_edges, binnumber = stats.binned_statistic(windspeed,
...                 boatspeed, statistic='median', bins=[1,2,3,4,5,6,7])
>>> plt.figure()
>>> plt.plot(windspeed, boatspeed, 'b.', label='raw data')
>>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=5,
...            label='binned statistic of data')
>>> plt.legend()

Now we can use ``binnumber`` to select all datapoints with a windspeed
below 1:

>>> low_boatspeed = boatspeed[binnumber == 0]

As a final example, we will use ``bin_edges`` and ``binnumber`` to make a
plot of a distribution that shows the mean and distribution around that
mean per bin, on top of a regular histogram and the probability
distribution function:

>>> x = np.linspace(0, 5, num=500)
>>> x_pdf = stats.maxwell.pdf(x)
>>> samples = stats.maxwell.rvs(size=10000)

>>> bin_means, bin_edges, binnumber = stats.binned_statistic(x, x_pdf,
...         statistic='mean', bins=25)
>>> bin_width = (bin_edges[1] - bin_edges[0])
>>> bin_centers = bin_edges[1:] - bin_width/2

>>> plt.figure()
>>> plt.hist(samples, bins=50, density=True, histtype='stepfilled',
...          alpha=0.2, label='histogram of data')
>>> plt.plot(x, x_pdf, 'r-', label='analytical pdf')
>>> plt.hlines(bin_means, bin_edges[:-1], bin_edges[1:], colors='g', lw=2,
...            label='binned statistic of data')
>>> plt.plot((binnumber - 0.5) * bin_width, x_pdf, 'g.', alpha=0.5)
>>> plt.legend(fontsize=10)
>>> plt.show()

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