1%feature("docstring") OT::ClaytonCopula
2"Clayton copula.
3
4Parameters
5----------
6theta : float
7    Parameter :math:`\theta`, :math:`\theta \geq -1`. Default is :math:`\theta=2`.
8
9Notes
10-----
11The Clayton copula is a bivariate asymmmetric Archimedean copula, exhibiting
12greater dependence in the negative tail than in the positive. It is defined by:
13
14.. math::
15
16    C(u_1, u_2) = (u_1^{-\theta} + u_2^{-\theta} - 1)^{-1/\theta}
17
18for :math:`(u_1, u_2) \in [0, 1]^2`
19
20And its generator is:
21
22.. math::
23
24    \varphi(t) = \frac{1}{\theta} (t^{-\theta} - 1)
25
26The support of the copula is :math:`\{ (u,v)\in [0,1]^2, u^{-\theta} +  v^{-\theta} \geq 1 \}`.
27
28If :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.
29
30See also
31--------
32ArchimedeanCopula
33
34Examples
35--------
36Create a distribution:
37
38>>> import openturns as ot
39>>> copula = ot.ClaytonCopula(2.5)
40
41Draw a sample:
42
43>>> sample = copula.getSample(5)"
44
45// ---------------------------------------------------------------------
46
47%feature("docstring") OT::ClaytonCopula::getTheta
48"Get the parameter :math:`\theta`.
49
50Returns
51-------
52theta : float
53    Parameter :math:`\theta` of the copula."
54
55// ---------------------------------------------------------------------
56
57%feature("docstring") OT::ClaytonCopula::setTheta
58"Set the parameter :math:`\theta`.
59
60Parameters
61----------
62theta : float
63    Parameter :math:`\theta` of the copula."
64