/usr/include/openturns/swig/OrdinalSumCopula_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 | %feature("docstring") OT::OrdinalSumCopula
"Copula built as an ordinal sum of copulas.
Available constructors:
OrdinalSumCopula(*collCopula, bounds*)
Parameters
----------
collCopula : list of :class:`~openturns.Distribution`
The collection :math:`(C_1, \\\\dots, C_n)` of :math:`n` copulas of dimension :math:`d`.
bounds : sequence of float, of size :math:`n-1` and :math:`0 \\\\leq \\\\alpha_1 \\\\leq \\\\dots \\\\leq \\\\alpha_{n-1} \\\\leq 1`
The bounds :math:`\\\\alpha_i` are such that the copula :math:`C_i` is
squeezed into :math:`[\\\\alpha_i, \\\\alpha_{i+1}]`.
Notes
-----
The ordinal sum of the :math:`n` copulas :math:`(C_1, \\\\dots, C_n)`, each one
being squeezed into the interval :math:`[\\\\alpha_i, \\\\alpha_{i+1}], i=1 \\\\dots n-1`,
writes:
.. math::
C(\\\\vect{u}) = \\\\left\\\\{
\\\\begin{array}{ll}
\\\\alpha_i+C_i \\\\left( \\\\dfrac{u_1-\\\\alpha_i}{\\\\alpha_{i+1} - \\\\alpha_i} \\\\right)
& \\\\mbox{ if } \\\\vect{u} \\\\in [\\\\alpha_i, \\\\alpha_{i+1}[ \\\\\\\\
M_d(\\\\vect{u}) & \\\\mbox{ else }
\\\\end{array}
\\\\right.
with :math:`M_d` the Min-copula: :math:`M_d(\\\\vect{u}) = \\\\min_{k=1 \\\\dots d} u_k`
and where, for convenience, we noted :math:`\\\\alpha_0=0` and :math:`\\\\alpha_n=1`.
Note that if :math:`\\\\alpha_i=\\\\alpha_{i+1}` then the copula :math:`C_{i+1}` is
erased from the list, for :math:`i=0 \\\\dots n-1`.
See also
--------
Copula
Examples
--------
Create a distribution:
>>> import openturns as ot
>>> ordinalSumCop = ot.OrdinalSumCopula([ot.GumbelCopula(2), ot.NormalCopula(2)], [0.3])
>>> graph = ordinalSumCop.drawPDF()
>>> graph.setTitle('Ordinal sum of copulas')"
// ---------------------------------------------------------------------
%feature("docstring") OT::OrdinalSumCopula::getCopulaCollection
"Accessor to the collection of copulas.
Returns
-------
copColl : list of :class:`~openturns.Copula` with the same dimension
List of copulas that build the ordinal sum."
// ---------------------------------------------------------------------
%feature("docstring") OT::OrdinalSumCopula::getBounds
"Accessor to the collection of bounds.
Returns
-------
bounds : :class:`~openturns.NumericalPoint`
Bounds defining the intervals on which the copulas of the collection are
squeezed."
// ---------------------------------------------------------------------
%feature("docstring") OT::OrdinalSumCopula::setCopulaCollection
"Accessor to the collection of copulas.
Parameters
----------
copColl : list of :class:`~openturns.Copula` with the same dimension
List of copulas that build the ordinal sum."
// ---------------------------------------------------------------------
%feature("docstring") OT::OrdinalSumCopula::setBounds
"Accessor to the collection of bounds.
Parameters
----------
bounds : sequence of float
Bounds defining the intervals on whch the copulas of the collection are
squeezed."
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