%feature("docstring") OT::GeneralizedPareto
"Generalized Pareto distribution.

Available constructors:
    GeneralizedPareto(*sigma=1.0, xi=0.0*)

Parameters
----------
sigma : float, :math:`\sigma > 0`
    Scale parameter :math:`\sigma`.
xi : float
    Shape parameter :math:`\xi`.

Notes
-----
Its cumulative distribution function is defined as:

.. math::

    F_X(x) = \left\{\begin{array}{ll}
               \displaystyle 1 - \left[1 + \xi \frac{x}{\sigma}\right]^{-1/\xi}
                    & \text{ if } \xi \neq 0 \\
               \displaystyle 1 - \exp\left(-\frac{x}{\sigma}\right)
                    & \text{ if } \xi = 0
            \end{array}\right.,
            \quad x \in [0; +\infty[

with :math:`\sigma > 0` and :math:`\xi \in \Rset`.

Its first moments are:

.. math::
    :nowrap:

    \begin{eqnarray*}
        \Expect{X} & = & \frac{\sigma}{1 - \xi}
                         \quad \text{ if } \xi < 1 \\
        \Var{X} & = & \frac{\sigma^2}{(1 - 2 \xi) (1 - \xi)^2}
                      \quad \text{ if } \xi < \frac{1}{2}
    \end{eqnarray*}

Examples
--------
Create a distribution:

>>> import openturns as ot
>>> distribution = ot.GeneralizedPareto(1.0, 0.0)

Draw a sample:

>>> sample = distribution.getSample(5)"

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%feature("docstring") OT::GeneralizedPareto::getSigma
"Accessor to the distribution's scale parameter :math:`\sigma`.

Returns
-------
sigma : float
    Scale parameter :math:`\sigma`."

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%feature("docstring") OT::GeneralizedPareto::getXi
"Accessor to the distribution's shape parameter :math:`\xi`.

Returns
-------
xi : float
    Shape parameter :math:`\xi`."

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%feature("docstring") OT::GeneralizedPareto::setSigma
"Accessor to the distribution's scale parameter :math:`\sigma`.

Parameters
----------
sigma : float, :math:`\sigma > 0`
    Scale parameter :math:`\sigma`."

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%feature("docstring") OT::GeneralizedPareto::setXi
"Accessor to the distribution's shape parameter :math:`\xi`.

Parameters
----------
xi : float, :math:`\xi \in \Rset`
    Shape parameter :math:`\xi`."
