/usr/include/openturns/swig/ClaytonCopula_doc.i is in libopenturns-dev 1.7-3.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 | %feature("docstring") OT::ClaytonCopula
"Clayton copula.
Available constructor:
ClaytonCopula(*theta=2.0*)
Parameters
----------
theta : float
Parameter :math:`\\\\theta`, :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(10)"
// ---------------------------------------------------------------------
%feature("docstring") OT::ClaytonCopula::getTheta
"Get the parameter :math:`\\\\theta`.
Returns
-------
theta : float
Parameter :math:`\\\\theta` of the copula."
// ---------------------------------------------------------------------
%feature("docstring") OT::ClaytonCopula::setTheta
"Set the parameter :math:`\\\\theta`.
Parameters
----------
theta : float
Parameter :math:`\\\\theta` of the copula."
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