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Fonction gennorm - module scipy.stats

Signature de la fonction gennorm

def gennorm(*args, **kwds) 

Description

gennorm.__doc__

A generalized normal continuous random variable.

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

    See Also
    --------
    laplace : Laplace distribution
    norm : normal distribution

    Notes
    -----
    The probability density function for `gennorm` is [1]_:

    .. math::

        f(x, \beta) = \frac{\beta}{2 \Gamma(1/\beta)} \exp(-|x|^\beta)

    :math:`\Gamma` is the gamma function (`scipy.special.gamma`).

    `gennorm` takes ``beta`` as a shape parameter for :math:`\beta`.
    For :math:`\beta = 1`, it is identical to a Laplace distribution.
    For :math:`\beta = 2`, it is identical to a normal distribution
    (with ``scale=1/sqrt(2)``).

    References
    ----------

    .. [1] "Generalized normal distribution, Version 1",
           https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1

    Examples
    --------
    >>> from scipy.stats import gennorm
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)
    
    Calculate the first four moments:
    
    >>> beta = 1.3
    >>> mean, var, skew, kurt = gennorm.stats(beta, moments='mvsk')
    
    Display the probability density function (``pdf``):
    
    >>> x = np.linspace(gennorm.ppf(0.01, beta),
    ...                 gennorm.ppf(0.99, beta), 100)
    >>> ax.plot(x, gennorm.pdf(x, beta),
    ...        'r-', lw=5, alpha=0.6, label='gennorm 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 = gennorm(beta)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
    
    Check accuracy of ``cdf`` and ``ppf``:
    
    >>> vals = gennorm.ppf([0.001, 0.5, 0.999], beta)
    >>> np.allclose([0.001, 0.5, 0.999], gennorm.cdf(vals, beta))
    True
    
    Generate random numbers:
    
    >>> r = gennorm.rvs(beta, size=1000)
    
    And compare the histogram:
    
    >>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()