Module « scipy.stats »

Fonction ncx2 - module scipy.stats

Signature de la fonction ncx2

def ncx2(*args, **kwds) 

Description

ncx2.__doc__

A non-central chi-squared continuous random variable.

    As an instance of the `rv_continuous` class, `ncx2` 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(df, nc, loc=0, scale=1, size=1, random_state=None)
        Random variates.
    pdf(x, df, nc, loc=0, scale=1)
        Probability density function.
    logpdf(x, df, nc, loc=0, scale=1)
        Log of the probability density function.
    cdf(x, df, nc, loc=0, scale=1)
        Cumulative distribution function.
    logcdf(x, df, nc, loc=0, scale=1)
        Log of the cumulative distribution function.
    sf(x, df, nc, loc=0, scale=1)
        Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
    logsf(x, df, nc, loc=0, scale=1)
        Log of the survival function.
    ppf(q, df, nc, loc=0, scale=1)
        Percent point function (inverse of ``cdf`` --- percentiles).
    isf(q, df, nc, loc=0, scale=1)
        Inverse survival function (inverse of ``sf``).
    moment(n, df, nc, loc=0, scale=1)
        Non-central moment of order n
    stats(df, nc, loc=0, scale=1, moments='mv')
        Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
    entropy(df, 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=(df, 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(df, nc, loc=0, scale=1)
        Median of the distribution.
    mean(df, nc, loc=0, scale=1)
        Mean of the distribution.
    var(df, nc, loc=0, scale=1)
        Variance of the distribution.
    std(df, nc, loc=0, scale=1)
        Standard deviation of the distribution.
    interval(alpha, df, nc, loc=0, scale=1)
        Endpoints of the range that contains fraction alpha [0, 1] of the
        distribution

    Notes
    -----
    The probability density function for `ncx2` is:

    .. math::

        f(x, k, \lambda) = \frac{1}{2} \exp(-(\lambda+x)/2)
            (x/\lambda)^{(k-2)/4}  I_{(k-2)/2}(\sqrt{\lambda x})

    for :math:`x >= 0` and :math:`k, \lambda > 0`. :math:`k` specifies the
    degrees of freedom (denoted ``df`` in the implementation) and
    :math:`\lambda` is the non-centrality parameter (denoted ``nc`` in the
    implementation). :math:`I_\nu` denotes the modified Bessel function of
    first order of degree :math:`\nu` (`scipy.special.iv`).

    `ncx2` takes ``df`` and ``nc`` 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, ``ncx2.pdf(x, df, nc, loc, scale)`` is identically
    equivalent to ``ncx2.pdf(y, df, 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 ncx2
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)
    
    Calculate the first four moments:
    
    >>> df, nc = 21, 1.06
    >>> mean, var, skew, kurt = ncx2.stats(df, nc, moments='mvsk')
    
    Display the probability density function (``pdf``):
    
    >>> x = np.linspace(ncx2.ppf(0.01, df, nc),
    ...                 ncx2.ppf(0.99, df, nc), 100)
    >>> ax.plot(x, ncx2.pdf(x, df, nc),
    ...        'r-', lw=5, alpha=0.6, label='ncx2 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 = ncx2(df, nc)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
    
    Check accuracy of ``cdf`` and ``ppf``:
    
    >>> vals = ncx2.ppf([0.001, 0.5, 0.999], df, nc)
    >>> np.allclose([0.001, 0.5, 0.999], ncx2.cdf(vals, df, nc))
    True
    
    Generate random numbers:
    
    >>> r = ncx2.rvs(df, 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()