Module « scipy.stats »

Fonction gausshyper - module scipy.stats

Signature de la fonction gausshyper

def gausshyper(*args, **kwds) 

Description

gausshyper.__doc__

A Gauss hypergeometric continuous random variable.

    As an instance of the `rv_continuous` class, `gausshyper` 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(a, b, c, z, loc=0, scale=1, size=1, random_state=None)
        Random variates.
    pdf(x, a, b, c, z, loc=0, scale=1)
        Probability density function.
    logpdf(x, a, b, c, z, loc=0, scale=1)
        Log of the probability density function.
    cdf(x, a, b, c, z, loc=0, scale=1)
        Cumulative distribution function.
    logcdf(x, a, b, c, z, loc=0, scale=1)
        Log of the cumulative distribution function.
    sf(x, a, b, c, z, loc=0, scale=1)
        Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
    logsf(x, a, b, c, z, loc=0, scale=1)
        Log of the survival function.
    ppf(q, a, b, c, z, loc=0, scale=1)
        Percent point function (inverse of ``cdf`` --- percentiles).
    isf(q, a, b, c, z, loc=0, scale=1)
        Inverse survival function (inverse of ``sf``).
    moment(n, a, b, c, z, loc=0, scale=1)
        Non-central moment of order n
    stats(a, b, c, z, loc=0, scale=1, moments='mv')
        Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
    entropy(a, b, c, z, loc=0, scale=1)
        (Differential) entropy of the RV.
    fit(data)
        Parameter estimates for generic data.
        See `scipy.stats.rv_continuous.fit <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit>`__ for detailed documentation of the
        keyword arguments.
    expect(func, args=(a, b, c, z), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)
        Expected value of a function (of one argument) with respect to the distribution.
    median(a, b, c, z, loc=0, scale=1)
        Median of the distribution.
    mean(a, b, c, z, loc=0, scale=1)
        Mean of the distribution.
    var(a, b, c, z, loc=0, scale=1)
        Variance of the distribution.
    std(a, b, c, z, loc=0, scale=1)
        Standard deviation of the distribution.
    interval(alpha, a, b, c, z, loc=0, scale=1)
        Endpoints of the range that contains fraction alpha [0, 1] of the
        distribution

    Notes
    -----
    The probability density function for `gausshyper` is:

    .. math::

        f(x, a, b, c, z) = C x^{a-1} (1-x)^{b-1} (1+zx)^{-c}

    for :math:`0 \le x \le 1`, :math:`a > 0`, :math:`b > 0`, :math:`z > -1`,
    and :math:`C = \frac{1}{B(a, b) F[2, 1](c, a; a+b; -z)}`.
    :math:`F[2, 1]` is the Gauss hypergeometric function
    `scipy.special.hyp2f1`.

    `gausshyper` takes :math:`a`, :math:`b`, :math:`c` and :math:`z` as shape
    parameters.

    The probability density above is defined in the "standardized" form. To shift
    and/or scale the distribution use the ``loc`` and ``scale`` parameters.
    Specifically, ``gausshyper.pdf(x, a, b, c, z, loc, scale)`` is identically
    equivalent to ``gausshyper.pdf(y, a, b, c, z) / scale`` with
    ``y = (x - loc) / scale``. Note that shifting the location of a distribution
    does not make it a "noncentral" distribution; noncentral generalizations of
    some distributions are available in separate classes.

    References
    ----------
    .. [1] Armero, C., and M. J. Bayarri. "Prior Assessments for Prediction in
           Queues." *Journal of the Royal Statistical Society*. Series D (The
           Statistician) 43, no. 1 (1994): 139-53. doi:10.2307/2348939

    Examples
    --------
    >>> from scipy.stats import gausshyper
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)
    
    Calculate the first four moments:
    
    >>> a, b, c, z = 13.8, 3.12, 2.51, 5.18
    >>> mean, var, skew, kurt = gausshyper.stats(a, b, c, z, moments='mvsk')
    
    Display the probability density function (``pdf``):
    
    >>> x = np.linspace(gausshyper.ppf(0.01, a, b, c, z),
    ...                 gausshyper.ppf(0.99, a, b, c, z), 100)
    >>> ax.plot(x, gausshyper.pdf(x, a, b, c, z),
    ...        'r-', lw=5, alpha=0.6, label='gausshyper pdf')
    
    Alternatively, the distribution object can be called (as a function)
    to fix the shape, location and scale parameters. This returns a "frozen"
    RV object holding the given parameters fixed.
    
    Freeze the distribution and display the frozen ``pdf``:
    
    >>> rv = gausshyper(a, b, c, z)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
    
    Check accuracy of ``cdf`` and ``ppf``:
    
    >>> vals = gausshyper.ppf([0.001, 0.5, 0.999], a, b, c, z)
    >>> np.allclose([0.001, 0.5, 0.999], gausshyper.cdf(vals, a, b, c, z))
    True
    
    Generate random numbers:
    
    >>> r = gausshyper.rvs(a, b, c, z, size=1000)
    
    And compare the histogram:
    
    >>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()