%feature("docstring") OT::JoeCopula
"Joe copula.

Parameters
----------
theta : float
    Parameter :math:`\theta > 0`. Default is :math:`\theta=0.5`.
psi1 : float
    Parameter :math:`\psi_1 \in [0, 1]`. Default is :math:`\psi_1=0.5`.
psi2 : float
    Parameter :math:`\psi_2 \in [0, 1]`. Default is :math:`\psi_2=0.5`.

Notes
-----
The Joe copula is a bivariate copula defined by:

.. math::

    C(u_1, u_2) = \exp\left[\log(u_1u_2)A\left(\dfrac{\log u_2}{\log u_1u_2}\right)\right]

for :math:`(u_1, u_2) \in [0, 1]^2`

Where :math:`A` is the following Pickand function 
:math:`t \in [0,1]`, :math:`A(t) = 1 - [ (\psi_1 (1-t))^{-1/ \theta} + (\psi_2 t)^{-1/ \theta} ]^{- \theta}`

See also
--------
ExtremeValueCopula

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

>>> import openturns as ot
>>> copula = ot.JoeCopula(0.5)

Draw a sample:

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

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

%feature("docstring") OT::JoeCopula::getTheta
"Get the Joe copula parameter :math:`\theta`.

Returns
-------
theta : float
    The scalar parameter :math:`\theta > 0`.
"

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

%feature("docstring") OT::JoeCopula::setTheta
"Set the Joe copula parameter :math:`\theta`.

Parameters
----------
theta : float
    The scalar parameter :math:`\theta > 0`.
"

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


%feature("docstring") OT::JoeCopula::getPsi1
"Get the Joe copula parameter :math:`\psi_1`.

Returns
-------
psi1 : float
    The scalar parameter :math:`\psi_1 \in [0, 1]`.
"

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

%feature("docstring") OT::JoeCopula::setPsi1
"Set the Joe copula parameter :math:`\psi_1`.

Parameters
----------
psi1 : float
    The scalar parameter :math:`\psi_1 \in [0, 1]`.
"

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

%feature("docstring") OT::JoeCopula::getPsi2
"Get the Joe copula parameter :math:`\psi_2`.

Returns
-------
psi2 : float
    The scalar parameter :math:`\psi_2 \in [0, 1]`.
"

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

%feature("docstring") OT::JoeCopula::setPsi2
"Set the Joe copula parameter :math:`\psi_2`.

Parameters
----------
psi2 : float
    The scalar parameter :math:`\psi_2 \in [0, 1]`.
"