%feature("docstring") OT::ClaytonCopula
"Clayton copula.

Available constructor:
    ClaytonCopula(*theta=2.0*)

Parameters
----------
theta : float
    Parameter :math:`\theta \geq -1`.

Notes
-----
The Clayton copula is a bivariate asymmmetric Archimedean copula, exhibiting
greater dependence in the negative tail than in the positive. It is defined by:

.. math::

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

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

And its generator is:

.. math::

    \varphi(t) = \frac{1}{\theta} (t^{-\theta} - 1)

The support of the copula is :math:`\{ (u,v)\in [0,1]^2, u^{-\theta} +  v^{-\theta} \geq 1 \}`. 

If :math:`\theta <0`, the support is strictly included in :math:`[0,1]^2` and the frontier defined by :math:`\{ (u,v)\in [0,1]^2, u^{-\theta} +  v^{-\theta} = 1 \}` has a mass not equal to zero. In that case, the copula is a non strict archimedean copula.

See also
--------
ArchimedeanCopula

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

>>> import openturns as ot
>>> copula = ot.ClaytonCopula(2.5)

Draw a sample:

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

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

Returns
-------
theta : float
    Parameter :math:`\theta` of the copula."

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

Parameters
----------
theta : float
    Parameter :math:`\theta` of the copula."
