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Fonction ncf - module scipy.stats

Signature de la fonction ncf

def ncf(*args, **kwds) 

Description

ncf.__doc__

A non-central F distribution continuous random variable.

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

    See Also
    --------
    scipy.stats.f : Fisher distribution

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

    .. math::

        f(x, n_1, n_2, \lambda) =
            \exp\left(\frac{\lambda}{2} +
                      \lambda n_1 \frac{x}{2(n_1 x + n_2)}
                \right)
            n_1^{n_1/2} n_2^{n_2/2} x^{n_1/2 - 1} \\
            (n_2 + n_1 x)^{-(n_1 + n_2)/2}
            \gamma(n_1/2) \gamma(1 + n_2/2) \\
            \frac{L^{\frac{n_1}{2}-1}_{n_2/2}
                \left(-\lambda n_1 \frac{x}{2(n_1 x + n_2)}\right)}
            {B(n_1/2, n_2/2)
                \gamma\left(\frac{n_1 + n_2}{2}\right)}

    for :math:`n_1, n_2 > 0`, :math:`\lambda \ge 0`.  Here :math:`n_1` is the
    degrees of freedom in the numerator, :math:`n_2` the degrees of freedom in
    the denominator, :math:`\lambda` the non-centrality parameter,
    :math:`\gamma` is the logarithm of the Gamma function, :math:`L_n^k` is a
    generalized Laguerre polynomial and :math:`B` is the beta function.

    `ncf` takes ``df1``, ``df2`` and ``nc`` as shape parameters. If ``nc=0``,
    the distribution becomes equivalent to the Fisher distribution.

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

    Examples
    --------
    >>> from scipy.stats import ncf
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)
    
    Calculate the first four moments:
    
    >>> dfn, dfd, nc = 27, 27, 0.416
    >>> mean, var, skew, kurt = ncf.stats(dfn, dfd, nc, moments='mvsk')
    
    Display the probability density function (``pdf``):
    
    >>> x = np.linspace(ncf.ppf(0.01, dfn, dfd, nc),
    ...                 ncf.ppf(0.99, dfn, dfd, nc), 100)
    >>> ax.plot(x, ncf.pdf(x, dfn, dfd, nc),
    ...        'r-', lw=5, alpha=0.6, label='ncf 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 = ncf(dfn, dfd, nc)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
    
    Check accuracy of ``cdf`` and ``ppf``:
    
    >>> vals = ncf.ppf([0.001, 0.5, 0.999], dfn, dfd, nc)
    >>> np.allclose([0.001, 0.5, 0.999], ncf.cdf(vals, dfn, dfd, nc))
    True
    
    Generate random numbers:
    
    >>> r = ncf.rvs(dfn, dfd, nc, size=1000)
    
    And compare the histogram:
    
    >>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()