are the same as for pdf calculation. The default cdf method can
be changed by setting ``levy_stable.cdf_default_method`` to either
'piecewise' or 'fft-simpson'.  For cdf calculations the Zolatarev method is
superior in accuracy, so FFT is disabled by default.

Fitting estimate uses quantile estimation method in [MC]. MLE estimation of
parameters in fit method uses this quantile estimate initially. Note that
MLE doesn't always converge if using FFT for pdf calculations; this will be
the case if alpha <= 1 where the FFT approach doesn't give good
approximations.

Any non-missing value for the attribute
``levy_stable.pdf_fft_min_points_threshold`` will set
``levy_stable.pdf_default_method`` to 'fft-simpson' if a valid
default method is not otherwise set.



.. warning::

    For pdf calculations FFT calculation is considered experimental.

    For cdf calculations FFT calculation is considered experimental. Use
    Zolatarev's method instead (default).

The probability density above is defined in the "standardized" form. To
shift and/or scale the distribution use the ``loc`` and ``scale``
parameters.
Generally ``%(name)s.pdf(x, %(shapes)s, loc, scale)`` is identically
equivalent to ``%(name)s.pdf(y, %(shapes)s) / scale`` with
``y = (x - loc) / scale``, except in the ``S1`` parameterization if
``alpha == 1``.  In that case ``%(name)s.pdf(x, %(shapes)s, loc, scale)``
is identically equivalent to ``%(name)s.pdf(y, %(shapes)s) / scale`` with
``y = (x - loc - 2 * beta * scale * np.log(scale) / np.pi) / scale``.
See [NO2]_ Definition 1.8 for more information.
Note that shifting the location of a distribution
does not make it a "noncentral" distribution.

References
----------
.. [MC] McCulloch, J., 1986. Simple consistent estimators of stable
    distribution parameters. Communications in Statistics - Simulation and
    Computation 15, 11091136.
.. [WZ] Wang, Li and Zhang, Ji-Hong, 2008. Simpson's rule based FFT method
    to compute densities of stable distribution.
.. [NO] Nolan, J., 1997. Numerical Calculation of Stable Densities and
    distributions Functions.
.. [NO2] Nolan, J., 2018. Stable Distributions: Models for Heavy Tailed
    Data.
.. [HO] Hopcraft, K. I., Jakeman, E., Tanner, R. M. J., 1999. Lévy random
    walks with fluctuating step number and multiscale behavior.

%(example)s

