/usr/include/openturns/swig/ConditionalDistribution_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 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 | %feature("docstring") OT::ConditionalDistribution
"Conditional distribution.
Helper class for defining the distribution of :math:`\\\\vect{X}` such that :math:`\\\\vect{X}|\\\\vect{\\\\Theta}` follows the distribution :math:`\\\\mathcal{L}_{\\\\vect{X}|\\\\vect{\\\\Theta}}`, with :math:`\\\\vect{\\\\Theta}=g(\\\\vect{Y})`, :math:`\\\\vect{Y}` follows the distribution :math:`\\\\mathcal{L}_{\\\\vect{Y}}` and :math:`g` is a given function of input dimension the dimension of :math:`\\\\mathcal{L}_{\\\\vect{Y}}` and output dimension the dimension of :math:`\\\\vect{\\\\Theta}`.
Available constructors:
ConditionalDistribution(*conditionedDist, conditioningDist, linkFunction*)
ConditionalDistribution(*conditionedDist, conditioningDist*)
ConditionalDistribution()
Parameters
----------
conditionedDist : :class:`~openturns.Distribution`, the distribution of :math:`\\\\vect{X}|\\\\vect{\\\\Theta}`, whose parameters will be overwritten by :math:`g(\\\\vect{Y})`.
In the `ConditionalDistribution()` constructor, `conditionedDist` is taken equal to :math:`\\\\vect{X} | \\\\vect{\\\\Theta} \\\\sim` :class:`~openturns.Uniform` :math:`(\\\\vect{\\\\Theta})`.
conditioningDist : :class:`~openturns.Distribution`, the distribution of :math:`\\\\vect{Y}`, specified with its parameters.
In the `ConditionalDistribution()` constructor, `conditioningDist` is taken equal to :math:`\\\\vect{Y} \\\\sim` :class:`~openturns.Uniform`:math:`(-1,1)`.
linkFunction : :class:`~openturns.NumericalMathFunction`, the function :math:`g: \\\\Rset^p \\\\rightarrow \\\\Rset^q`, where :math:`p` is the dimension of `conditioningDist` and :math:`q` is the dimension of :math:`\\\\vect{\\\\Theta}`.
In the `ConditionalDistribution()` constructor, `linkFunction` is taken equal to :math:`g: \\\\Rset \\\\rightarrow \\\\Rset^2` with :math:`g(y)=(y,y+1)`.
In the `ConditionalDistribution(conditionedDist, conditioningDist)` constructor, we need :math:`p=q` and `linkFunction` is taken equal to :math:`g(\\\\vect{y})=\\\\vect{y}`.
Notes
-----
Its probability density function is defined as:
.. math::
f_{\\\\vect{X}}(\\\\vect{x}) = \\\\int f_{\\\\vect{X}|\\\\vect{\\\\Theta}=g(\\\\vect{y})}(\\\\vect{x}|g(\\\\vect{y})) f_{\\\\vect{Y}}(\\\\vect{y})\\\\, d\\\\vect{y}
with :math:`f_{\\\\vect{X}|\\\\vect{\\\\Theta}=g(\\\\vect{y})}` the PDF of the distribution of :math:`\\\\vect{X}|\\\\vect{\\\\Theta}`, where :math:`\\\\vect{\\\\Theta}` has been replaced by :math:`g(\\\\vect{y})`, :math:`f_{\\\\vect{Y}}` the PDF of :math:`\\\\vect{Y}` and :math:`g` the linking function.
With the default constructor, the resulting random variable :math:`X` follows a trapezoidal distribution parametered by :math:`(-1, 0, 1, 2)`.
Note that a :class:`~openturns.ConditionalDistribution` can be obtained as the first marginal distribution of a :class:`~openturns.BayesDistribution`.
Examples
--------
Create a distribution:
>>> import openturns as ot
>>> conditioningDist = ot.Normal(0.0, 1.0)
>>> g = ot.NumericalMathFunction(['y'], ['y', '0.1+y^2'])
>>> conditionedDist = ot.Normal()
>>> finalDist = ot.ConditionalDistribution(conditionedDist, conditioningDist, g)
Draw a sample:
>>> sample = finalDist.getSample(10)
"
// ---------------------------------------------------------------------
%feature("docstring") OT::ConditionalDistribution::getConditionedDistribution
"Accessor to the distribution's conditioned distribution parameter `conditionedDistribution`.
Returns
-------
conditionedDistribution : :class:`~openturns.Distribution`, the distribution of :math:`\\\\vect{X}|\\\\vect{\\\\Theta}`, whose parameters will be overwritten by :math:`g(\\\\vect{Y})`.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::ConditionalDistribution::getConditioningDistribution
"Accessor to the distribution's conditioned distribution parameter `conditioningDistribution`.
Returns
-------
conditioningDistribution : :class:`~openturns.Distribution`, the distribution of :math:`\\\\vect{Y}`, specified with its parameters.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::ConditionalDistribution::getLinkFunction
"Accessor to the distribution's conditioned distribution parameter `linkFunction`.
Returns
-------
linkFunction : :class:`~openturns.NumericalMathFunction`, the function :math:`g: \\\\Rset^p \\\\rightarrow \\\\Rset^q`, where :math:`p` is the dimension of `conditioningDist` and :math:`q` is the dimension of :math:`\\\\vect{\\\\Theta}`.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::ConditionalDistribution::setConditionedDistribution
"Accessor to the distribution's conditioned distribution parameter `conditionedDistribution`.
Parameters
----------
conditionedDistribution : :class:`~openturns.Distribution`, the distribution of :math:`\\\\vect{X}|\\\\vect{\\\\Theta}`, whose parameters will be overwritten by :math:`g(\\\\vect{Y})`.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::ConditionalDistribution::setConditioningDistribution
"Accessor to the distribution's conditioned distribution parameter `conditioningDistribution`.
Parameters
----------
conditioningDistribution : :class:`~openturns.Distribution`, the distribution of :math:`\\\\vect{Y}`, specified with its parameters.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::ConditionalDistribution::setLinkFunction
"Accessor to the distribution's conditioned distribution parameter `linkFunction`.
Parameters
----------
linkFunction : :class:`~openturns.NumericalMathFunction`, the function :math:`g: \\\\Rset^p \\\\rightarrow \\\\Rset^q`, where :math:`p` is the dimension of `conditioningDist` and :math:`q` is the dimension of :math:`\\\\vect{\\\\Theta}`.
"
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