%feature("docstring") OT::ArchimedeanCopula
"Base class for bivariate Archimedean copulas.

Notes
-----
The bivariate Archimedean copulas are defined by:

.. math::

    C(u_1, u_2; \theta) = \varphi^{-1}(\varphi(u_1; \theta) + \varphi(u_2; \theta); \theta)

where :math:`\varphi` is the generator of the copula, a continous, strictly
decreasing and convex function from :math:`[0, 1]\times \theta` to
:math:`[0, \infty)` such that :math:`\varphi(1; \theta)=0`. :math:`\varphi^{-1}`
is the pseudo-inverse of the generator function defined by:

.. math::

    \varphi^{-1}(t; \theta) = \left\{
                      \begin{array}{ll}
                      \displaystyle \varphi^{-1}(t; \theta)
                          & \text{ if } 0 \leq t \leq \varphi(0; \theta)\\
                      \displaystyle 0 & \text{ if } \varphi(0; \theta) \leq t \leq \infty
                      \end{array}
                              \right.


An ArchimedeanCopula object can be used only through its derived classes:

- :class:`~openturns.AliMikhailHaqCopula`
- :class:`~openturns.ClaytonCopula`
- :class:`~openturns.FrankCopula`
- :class:`~openturns.GumbelCopula`

See also
--------
Copula"

// ---------------------------------------------------------------------

%feature("docstring") OT::ArchimedeanCopula::computeArchimedeanGenerator
"Compute the Archimedean generator :math:`\varphi`.

Parameters
----------
t : float

Returns
-------
result : float
    The Archimedean generator :math:`\varphi`."

// ---------------------------------------------------------------------

%feature("docstring") OT::ArchimedeanCopula::computeArchimedeanGeneratorDerivative
"Compute the derivative of the Archimedean generator.

Parameters
----------
t : float

Returns
-------
result : float
    The derivative of the Archimedean generator :math:`\varphi`."

// ---------------------------------------------------------------------

%feature("docstring") OT::ArchimedeanCopula::computeArchimedeanGeneratorSecondDerivative
"Compute the seconde derivative of the Archimedean generator.

Parameters
----------
t : float

Returns
-------
result : float
    The seconde derivative of the Archimedean generator :math:`\varphi`."

// ---------------------------------------------------------------------

%feature("docstring") OT::ArchimedeanCopula::computeInverseArchimedeanGenerator
"Compute the inverse of the Archimedean generator.

Parameters
----------
t : float

Returns
-------
result : float
     :math:`\varphi^{-1}` the inverse of the Archimedean generator."