/usr/include/openturns/swig/ArchimedeanCopula_doc.i is in libopenturns-dev 1.7-3.
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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 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 | %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."
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