Module « scipy.stats »

Fonction betabinom - module scipy.stats

Signature de la fonction betabinom

def betabinom(*args, **kwds) 

Description

betabinom.__doc__

A beta-binomial discrete random variable.

    As an instance of the `rv_discrete` class, `betabinom` 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(alpha, n, a, b, loc=0)
        Endpoints of the range that contains fraction alpha [0, 1] of the
        distribution

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

    The probability mass function for `betabinom` is:

    .. math::

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

    for :math:`k \in \{0, 1, \dots, n\}`, :math:`n \geq 0`, :math:`a > 0`,
    :math:`b > 0`, where :math:`B(a, b)` is the beta function.

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

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

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

    .. versionadded:: 1.4.0

    See Also
    --------
    beta, binom

    Examples
    --------
    >>> from scipy.stats import betabinom
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)
    
    Calculate the first four moments:
    
    >>> n, a, b = 5, 2.3, 0.63
    >>> mean, var, skew, kurt = betabinom.stats(n, a, b, moments='mvsk')
    
    Display the probability mass function (``pmf``):
    
    >>> x = np.arange(betabinom.ppf(0.01, n, a, b),
    ...               betabinom.ppf(0.99, n, a, b))
    >>> ax.plot(x, betabinom.pmf(x, n, a, b), 'bo', ms=8, label='betabinom pmf')
    >>> ax.vlines(x, 0, betabinom.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 = betabinom(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 = betabinom.cdf(x, n, a, b)
    >>> np.allclose(x, betabinom.ppf(prob, n, a, b))
    True
    
    Generate random numbers:
    
    >>> r = betabinom.rvs(n, a, b, size=1000)