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Module « scipy.stats »

Fonction betanbinom - module scipy.stats

Signature de la fonction betanbinom

def betanbinom(*args, **kwds) 

Description

help(scipy.stats.betanbinom)

A beta-negative-binomial discrete random variable.

As an instance of the `rv_discrete` class, `betanbinom` object inherits from it
a collection of generic methods (see below for the full list),
and completes them with details specific for this particular distribution.

Methods
-------
rvs(n, a, b, loc=0, size=1, random_state=None)
    Random variates.
pmf(k, n, a, b, loc=0)
    Probability mass function.
logpmf(k, n, a, b, loc=0)
    Log of the probability mass function.
cdf(k, n, a, b, loc=0)
    Cumulative distribution function.
logcdf(k, n, a, b, loc=0)
    Log of the cumulative distribution function.
sf(k, n, a, b, loc=0)
    Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
logsf(k, n, a, b, loc=0)
    Log of the survival function.
ppf(q, n, a, b, loc=0)
    Percent point function (inverse of ``cdf`` --- percentiles).
isf(q, n, a, b, loc=0)
    Inverse survival function (inverse of ``sf``).
stats(n, a, b, loc=0, moments='mv')
    Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
entropy(n, a, b, loc=0)
    (Differential) entropy of the RV.
expect(func, args=(n, a, b), loc=0, lb=None, ub=None, conditional=False)
    Expected value of a function (of one argument) with respect to the distribution.
median(n, a, b, loc=0)
    Median of the distribution.
mean(n, a, b, loc=0)
    Mean of the distribution.
var(n, a, b, loc=0)
    Variance of the distribution.
std(n, a, b, loc=0)
    Standard deviation of the distribution.
interval(confidence, n, a, b, loc=0)
    Confidence interval with equal areas around the median.

Notes
-----
The beta-negative-binomial distribution is a negative binomial
distribution with a probability of success `p` that follows a
beta distribution.

The probability mass function for `betanbinom` is:

.. math::

   f(k) = \binom{n + k - 1}{k} \frac{B(a + n, b + k)}{B(a, b)}

for :math:`k \ge 0`, :math:`n \geq 0`, :math:`a > 0`,
:math:`b > 0`, where :math:`B(a, b)` is the beta function.

`betanbinom` takes :math:`n`, :math:`a`, and :math:`b` as shape parameters.

References
----------
.. [1] https://en.wikipedia.org/wiki/Beta_negative_binomial_distribution

The probability mass function above is defined in the "standardized" form.
To shift distribution use the ``loc`` parameter.
Specifically, ``betanbinom.pmf(k, n, a, b, loc)`` is identically
equivalent to ``betanbinom.pmf(k - loc, n, a, b)``.

.. versionadded:: 1.12.0

See Also
--------
betabinom : Beta binomial distribution

Examples
--------
>>> import numpy as np
>>> from scipy.stats import betanbinom
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Calculate the first four moments:

>>> n, a, b = 5, 9.3, 1
>>> mean, var, skew, kurt = betanbinom.stats(n, a, b, moments='mvsk')

Display the probability mass function (``pmf``):

>>> x = np.arange(betanbinom.ppf(0.01, n, a, b),
...               betanbinom.ppf(0.99, n, a, b))
>>> ax.plot(x, betanbinom.pmf(x, n, a, b), 'bo', ms=8, label='betanbinom pmf')
>>> ax.vlines(x, 0, betanbinom.pmf(x, n, a, b), colors='b', lw=5, alpha=0.5)

Alternatively, the distribution object can be called (as a function)
to fix the shape and location. This returns a "frozen" RV object holding
the given parameters fixed.

Freeze the distribution and display the frozen ``pmf``:

>>> rv = betanbinom(n, a, b)
>>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,
...         label='frozen pmf')
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

Check accuracy of ``cdf`` and ``ppf``:

>>> prob = betanbinom.cdf(x, n, a, b)
>>> np.allclose(x, betanbinom.ppf(prob, n, a, b))
True

Generate random numbers:

>>> r = betanbinom.rvs(n, a, b, size=1000)

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