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Fonction geninvgauss - module scipy.stats

Signature de la fonction geninvgauss

def geninvgauss(*args, **kwds) 

Description

geninvgauss.__doc__

A Generalized Inverse Gaussian continuous random variable.

    As an instance of the `rv_continuous` class, `geninvgauss` 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(p, b, loc=0, scale=1, size=1, random_state=None)
        Random variates.
    pdf(x, p, b, loc=0, scale=1)
        Probability density function.
    logpdf(x, p, b, loc=0, scale=1)
        Log of the probability density function.
    cdf(x, p, b, loc=0, scale=1)
        Cumulative distribution function.
    logcdf(x, p, b, loc=0, scale=1)
        Log of the cumulative distribution function.
    sf(x, p, b, loc=0, scale=1)
        Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
    logsf(x, p, b, loc=0, scale=1)
        Log of the survival function.
    ppf(q, p, b, loc=0, scale=1)
        Percent point function (inverse of ``cdf`` --- percentiles).
    isf(q, p, b, loc=0, scale=1)
        Inverse survival function (inverse of ``sf``).
    moment(n, p, b, loc=0, scale=1)
        Non-central moment of order n
    stats(p, b, loc=0, scale=1, moments='mv')
        Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
    entropy(p, b, 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=(p, b), 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(p, b, loc=0, scale=1)
        Median of the distribution.
    mean(p, b, loc=0, scale=1)
        Mean of the distribution.
    var(p, b, loc=0, scale=1)
        Variance of the distribution.
    std(p, b, loc=0, scale=1)
        Standard deviation of the distribution.
    interval(alpha, p, b, loc=0, scale=1)
        Endpoints of the range that contains fraction alpha [0, 1] of the
        distribution

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

    .. math::

        f(x, p, b) = x^{p-1} \exp(-b (x + 1/x) / 2) / (2 K_p(b))

    where `x > 0`, and the parameters `p, b` satisfy `b > 0` ([1]_).
    :math:`K_p` is the modified Bessel function of second kind of order `p`
    (`scipy.special.kv`).

    The probability density above is defined in the "standardized" form. To shift
    and/or scale the distribution use the ``loc`` and ``scale`` parameters.
    Specifically, ``geninvgauss.pdf(x, p, b, loc, scale)`` is identically
    equivalent to ``geninvgauss.pdf(y, p, b) / 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.

    The inverse Gaussian distribution `stats.invgauss(mu)` is a special case of
    `geninvgauss` with `p = -1/2`, `b = 1 / mu` and `scale = mu`.

    Generating random variates is challenging for this distribution. The
    implementation is based on [2]_.

    References
    ----------
    .. [1] O. Barndorff-Nielsen, P. Blaesild, C. Halgreen, "First hitting time
       models for the generalized inverse gaussian distribution",
       Stochastic Processes and their Applications 7, pp. 49--54, 1978.

    .. [2] W. Hoermann and J. Leydold, "Generating generalized inverse Gaussian
       random variates", Statistics and Computing, 24(4), p. 547--557, 2014.

    Examples
    --------
    >>> from scipy.stats import geninvgauss
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)
    
    Calculate the first four moments:
    
    >>> p, b = 2.3, 1.5
    >>> mean, var, skew, kurt = geninvgauss.stats(p, b, moments='mvsk')
    
    Display the probability density function (``pdf``):
    
    >>> x = np.linspace(geninvgauss.ppf(0.01, p, b),
    ...                 geninvgauss.ppf(0.99, p, b), 100)
    >>> ax.plot(x, geninvgauss.pdf(x, p, b),
    ...        'r-', lw=5, alpha=0.6, label='geninvgauss 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 = geninvgauss(p, b)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
    
    Check accuracy of ``cdf`` and ``ppf``:
    
    >>> vals = geninvgauss.ppf([0.001, 0.5, 0.999], p, b)
    >>> np.allclose([0.001, 0.5, 0.999], geninvgauss.cdf(vals, p, b))
    True
    
    Generate random numbers:
    
    >>> r = geninvgauss.rvs(p, b, size=1000)
    
    And compare the histogram:
    
    >>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()