Classe « rv_continuous »

Méthode scipy.stats.rv_continuous.fit

Signature de la méthode fit

def fit(self, data, *args, **kwds) 

Description

fit.__doc__

        Return estimates of shape (if applicable), location, and scale
        parameters from data. The default estimation method is Maximum
        Likelihood Estimation (MLE), but Method of Moments (MM)
        is also available.

        Starting estimates for
        the fit are given by input arguments; for any arguments not provided
        with starting estimates, ``self._fitstart(data)`` is called to generate
        such.

        One can hold some parameters fixed to specific values by passing in
        keyword arguments ``f0``, ``f1``, ..., ``fn`` (for shape parameters)
        and ``floc`` and ``fscale`` (for location and scale parameters,
        respectively).

        Parameters
        ----------
        data : array_like
            Data to use in estimating the distribution parameters.
        arg1, arg2, arg3,... : floats, optional
            Starting value(s) for any shape-characterizing arguments (those not
            provided will be determined by a call to ``_fitstart(data)``).
            No default value.
        kwds : floats, optional
            - `loc`: initial guess of the distribution's location parameter.
            - `scale`: initial guess of the distribution's scale parameter.

            Special keyword arguments are recognized as holding certain
            parameters fixed:

            - f0...fn : hold respective shape parameters fixed.
              Alternatively, shape parameters to fix can be specified by name.
              For example, if ``self.shapes == "a, b"``, ``fa`` and ``fix_a``
              are equivalent to ``f0``, and ``fb`` and ``fix_b`` are
              equivalent to ``f1``.

            - floc : hold location parameter fixed to specified value.

            - fscale : hold scale parameter fixed to specified value.

            - optimizer : The optimizer to use.
              The optimizer must take ``func``,
              and starting position as the first two arguments,
              plus ``args`` (for extra arguments to pass to the
              function to be optimized) and ``disp=0`` to suppress
              output as keyword arguments.

            - method : The method to use. The default is "MLE" (Maximum
              Likelihood Estimate); "MM" (Method of Moments)
              is also available.


        Returns
        -------
        parameter_tuple : tuple of floats
            Estimates for any shape parameters (if applicable),
            followed by those for location and scale.
            For most random variables, shape statistics
            will be returned, but there are exceptions (e.g. ``norm``).

        Notes
        -----
        With ``method="MLE"`` (default), the fit is computed by minimizing
        the negative log-likelihood function. A large, finite penalty
        (rather than infinite negative log-likelihood) is applied for
        observations beyond the support of the distribution.

        With ``method="MM"``, the fit is computed by minimizing the L2 norm
        of the relative errors between the first *k* raw (about zero) data
        moments and the corresponding distribution moments, where *k* is the
        number of non-fixed parameters.
        More precisely, the objective function is::

            (((data_moments - dist_moments)
              / np.maximum(np.abs(data_moments), 1e-8))**2).sum()

        where the constant ``1e-8`` avoids division by zero in case of
        vanishing data moments. Typically, this error norm can be reduced to
        zero.
        Note that the standard method of moments can produce parameters for
        which some data are outside the support of the fitted distribution;
        this implementation does nothing to prevent this.

        For either method,
        the returned answer is not guaranteed to be globally optimal; it
        may only be locally optimal, or the optimization may fail altogether.
        If the data contain any of ``np.nan``, ``np.inf``, or ``-np.inf``,
        the `fit` method will raise a ``RuntimeError``.

        Examples
        --------

        Generate some data to fit: draw random variates from the `beta`
        distribution

        >>> from scipy.stats import beta
        >>> a, b = 1., 2.
        >>> x = beta.rvs(a, b, size=1000)

        Now we can fit all four parameters (``a``, ``b``, ``loc``
        and ``scale``):

        >>> a1, b1, loc1, scale1 = beta.fit(x)

        We can also use some prior knowledge about the dataset: let's keep
        ``loc`` and ``scale`` fixed:

        >>> a1, b1, loc1, scale1 = beta.fit(x, floc=0, fscale=1)
        >>> loc1, scale1
        (0, 1)

        We can also keep shape parameters fixed by using ``f``-keywords. To
        keep the zero-th shape parameter ``a`` equal 1, use ``f0=1`` or,
        equivalently, ``fa=1``:

        >>> a1, b1, loc1, scale1 = beta.fit(x, fa=1, floc=0, fscale=1)
        >>> a1
        1

        Not all distributions return estimates for the shape parameters.
        ``norm`` for example just returns estimates for location and scale:

        >>> from scipy.stats import norm
        >>> x = norm.rvs(a, b, size=1000, random_state=123)
        >>> loc1, scale1 = norm.fit(x)
        >>> loc1, scale1
        (0.92087172783841631, 2.0015750750324668)