Module « scipy.stats »

Fonction probplot - module scipy.stats

Signature de la fonction probplot

def probplot(x, sparams=(), dist='norm', fit=True, plot=None, rvalue=False) 

Description

probplot.__doc__

    Calculate quantiles for a probability plot, and optionally show the plot.

    Generates a probability plot of sample data against the quantiles of a
    specified theoretical distribution (the normal distribution by default).
    `probplot` optionally calculates a best-fit line for the data and plots the
    results using Matplotlib or a given plot function.

    Parameters
    ----------
    x : array_like
        Sample/response data from which `probplot` creates the plot.
    sparams : tuple, optional
        Distribution-specific shape parameters (shape parameters plus location
        and scale).
    dist : str or stats.distributions instance, optional
        Distribution or distribution function name. The default is 'norm' for a
        normal probability plot.  Objects that look enough like a
        stats.distributions instance (i.e. they have a ``ppf`` method) are also
        accepted.
    fit : bool, optional
        Fit a least-squares regression (best-fit) line to the sample data if
        True (default).
    plot : object, optional
        If given, plots the quantiles.
        If given and `fit` is True, also plots the least squares fit.
        `plot` is an object that has to have methods "plot" and "text".
        The `matplotlib.pyplot` module or a Matplotlib Axes object can be used,
        or a custom object with the same methods.
        Default is None, which means that no plot is created.

    Returns
    -------
    (osm, osr) : tuple of ndarrays
        Tuple of theoretical quantiles (osm, or order statistic medians) and
        ordered responses (osr).  `osr` is simply sorted input `x`.
        For details on how `osm` is calculated see the Notes section.
    (slope, intercept, r) : tuple of floats, optional
        Tuple  containing the result of the least-squares fit, if that is
        performed by `probplot`. `r` is the square root of the coefficient of
        determination.  If ``fit=False`` and ``plot=None``, this tuple is not
        returned.

    Notes
    -----
    Even if `plot` is given, the figure is not shown or saved by `probplot`;
    ``plt.show()`` or ``plt.savefig('figname.png')`` should be used after
    calling `probplot`.

    `probplot` generates a probability plot, which should not be confused with
    a Q-Q or a P-P plot.  Statsmodels has more extensive functionality of this
    type, see ``statsmodels.api.ProbPlot``.

    The formula used for the theoretical quantiles (horizontal axis of the
    probability plot) is Filliben's estimate::

        quantiles = dist.ppf(val), for

                0.5**(1/n),                  for i = n
          val = (i - 0.3175) / (n + 0.365),  for i = 2, ..., n-1
                1 - 0.5**(1/n),              for i = 1

    where ``i`` indicates the i-th ordered value and ``n`` is the total number
    of values.

    Examples
    --------
    >>> from scipy import stats
    >>> import matplotlib.pyplot as plt
    >>> nsample = 100
    >>> rng = np.random.default_rng()

    A t distribution with small degrees of freedom:

    >>> ax1 = plt.subplot(221)
    >>> x = stats.t.rvs(3, size=nsample, random_state=rng)
    >>> res = stats.probplot(x, plot=plt)

    A t distribution with larger degrees of freedom:

    >>> ax2 = plt.subplot(222)
    >>> x = stats.t.rvs(25, size=nsample, random_state=rng)
    >>> res = stats.probplot(x, plot=plt)

    A mixture of two normal distributions with broadcasting:

    >>> ax3 = plt.subplot(223)
    >>> x = stats.norm.rvs(loc=[0,5], scale=[1,1.5],
    ...                    size=(nsample//2,2), random_state=rng).ravel()
    >>> res = stats.probplot(x, plot=plt)

    A standard normal distribution:

    >>> ax4 = plt.subplot(224)
    >>> x = stats.norm.rvs(loc=0, scale=1, size=nsample, random_state=rng)
    >>> res = stats.probplot(x, plot=plt)

    Produce a new figure with a loggamma distribution, using the ``dist`` and
    ``sparams`` keywords:

    >>> fig = plt.figure()
    >>> ax = fig.add_subplot(111)
    >>> x = stats.loggamma.rvs(c=2.5, size=500, random_state=rng)
    >>> res = stats.probplot(x, dist=stats.loggamma, sparams=(2.5,), plot=ax)
    >>> ax.set_title("Probplot for loggamma dist with shape parameter 2.5")

    Show the results with Matplotlib:

    >>> plt.show()