Classe « rv_histogram »

Informations générales

Héritage

builtins.object
    rv_generic
        rv_continuous
            rv_histogram

Définition

class rv_histogram(rv_continuous):

help(rv_histogram)

Generates a distribution given by a histogram.
This is useful to generate a template distribution from a binned
datasample.

As a subclass of the `rv_continuous` class, `rv_histogram` inherits from it
a collection of generic methods (see `rv_continuous` for the full list),
and implements them based on the properties of the provided binned
datasample.

Parameters
----------
histogram : tuple of array_like
    Tuple containing two array_like objects.
    The first containing the content of n bins,
    the second containing the (n+1) bin boundaries.
    In particular, the return value of `numpy.histogram` is accepted.

density : bool, optional
    If False, assumes the histogram is proportional to counts per bin;
    otherwise, assumes it is proportional to a density.
    For constant bin widths, these are equivalent, but the distinction
    is important when bin widths vary (see Notes).
    If None (default), sets ``density=True`` for backwards compatibility,
    but warns if the bin widths are variable. Set `density` explicitly
    to silence the warning.

    .. versionadded:: 1.10.0

Notes
-----
When a histogram has unequal bin widths, there is a distinction between
histograms that are proportional to counts per bin and histograms that are
proportional to probability density over a bin. If `numpy.histogram` is
called with its default ``density=False``, the resulting histogram is the
number of counts per bin, so ``density=False`` should be passed to
`rv_histogram`. If `numpy.histogram` is called with ``density=True``, the
resulting histogram is in terms of probability density, so ``density=True``
should be passed to `rv_histogram`. To avoid warnings, always pass
``density`` explicitly when the input histogram has unequal bin widths.

There are no additional shape parameters except for the loc and scale.
The pdf is defined as a stepwise function from the provided histogram.
The cdf is a linear interpolation of the pdf.

.. versionadded:: 0.19.0

Examples
--------

Create a scipy.stats distribution from a numpy histogram

>>> import scipy.stats
>>> import numpy as np
>>> data = scipy.stats.norm.rvs(size=100000, loc=0, scale=1.5,
...                             random_state=123)
>>> hist = np.histogram(data, bins=100)
>>> hist_dist = scipy.stats.rv_histogram(hist, density=False)

Behaves like an ordinary scipy rv_continuous distribution

>>> hist_dist.pdf(1.0)
0.20538577847618705
>>> hist_dist.cdf(2.0)
0.90818568543056499

PDF is zero above (below) the highest (lowest) bin of the histogram,
defined by the max (min) of the original dataset

>>> hist_dist.pdf(np.max(data))
0.0
>>> hist_dist.cdf(np.max(data))
1.0
>>> hist_dist.pdf(np.min(data))
7.7591907244498314e-05
>>> hist_dist.cdf(np.min(data))
0.0

PDF and CDF follow the histogram

>>> import matplotlib.pyplot as plt
>>> X = np.linspace(-5.0, 5.0, 100)
>>> fig, ax = plt.subplots()
>>> ax.set_title("PDF from Template")
>>> ax.hist(data, density=True, bins=100)
>>> ax.plot(X, hist_dist.pdf(X), label='PDF')
>>> ax.plot(X, hist_dist.cdf(X), label='CDF')
>>> ax.legend()
>>> fig.show()