# RandomVector¶

class RandomVector(*args)

Random vectors.

Parameters
distributionDistribution

Distribution of the UsualRandomVector to define.

Notes

A RandomVector provides at least a way to generate realizations.

Methods

 getAntecedent(self) Accessor to the antecedent RandomVector in case of a composite RandomVector. getClassName(self) Accessor to the object’s name. getCovariance(self) Accessor to the covariance of the RandomVector. getDescription(self) Accessor to the description of the RandomVector. getDimension(self) Accessor to the dimension of the RandomVector. getDistribution(self) Accessor to the distribution of the RandomVector. getDomain(self) Accessor to the domain of the Event. getFunction(self) Accessor to the Function in case of a composite RandomVector. getId(self) Accessor to the object’s id. getImplementation(self) Accessor to the underlying implementation. getMarginal(self, \*args) Get the random vector corresponding to the marginal component(s). getMean(self) Accessor to the mean of the RandomVector. getName(self) Accessor to the object’s name. getOperator(self) Accessor to the comparaison operator of the Event. getParameter(self) Accessor to the parameter of the distribution. getParameterDescription(self) Accessor to the parameter description of the distribution. getRealization(self) Compute one realization of the RandomVector. getSample(self, size) Compute realizations of the RandomVector. getThreshold(self) Accessor to the threshold of the Event. intersect(self, other) Intersection of two events. isComposite(self) Accessor to know if the RandomVector is a composite one. isEvent(self) Whether the random vector is an event. join(self, other) Union of two events. setDescription(self, description) Accessor to the description of the RandomVector. setName(self, name) Accessor to the object’s name. setParameter(self, parameters) Accessor to the parameter of the distribution.
__init__(self, \*args)

Initialize self. See help(type(self)) for accurate signature.

getAntecedent(self)

Accessor to the antecedent RandomVector in case of a composite RandomVector.

Returns
antecedentRandomVector

Antecedent RandomVector in case of a CompositeRandomVector such as: .

getClassName(self)

Accessor to the object’s name.

Returns
class_namestr

The object class name (object.__class__.__name__).

getCovariance(self)

Accessor to the covariance of the RandomVector.

Returns
covarianceCovarianceMatrix

Covariance of the considered UsualRandomVector.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.5], [1.0, 1.5], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getCovariance())
[[ 1    0    ]
[ 0    2.25 ]]
getDescription(self)

Accessor to the description of the RandomVector.

Returns
descriptionDescription

Describes the components of the RandomVector.

getDimension(self)

Accessor to the dimension of the RandomVector.

Returns
dimensionpositive int

Dimension of the RandomVector.

getDistribution(self)

Accessor to the distribution of the RandomVector.

Returns
distributionDistribution

Distribution of the considered UsualRandomVector.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.0], [1.0, 1.0], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getDistribution())
Normal(mu = [0,0], sigma = [1,1], R = [[ 1 0 ]
[ 0 1 ]])
getDomain(self)

Accessor to the domain of the Event.

Returns
domainDomain

Describes the domain of an event.

getFunction(self)

Accessor to the Function in case of a composite RandomVector.

Returns
functionFunction

Function used to define a CompositeRandomVector as the image through this function of the antecedent : .

getId(self)

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getImplementation(self)

Accessor to the underlying implementation.

Returns
implImplementation

The implementation class.

getMarginal(self, \*args)

Get the random vector corresponding to the marginal component(s).

Parameters
iint or list of ints,

Indicates the component(s) concerned. is the dimension of the RandomVector.

Returns
vectorRandomVector

RandomVector restricted to the concerned components.

Notes

Let’s note a random vector and a set of indices. If is a UsualRandomVector, the subvector is defined by . If is a CompositeRandomVector, defined by with , some scalar functions, the subvector is .

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.0], [1.0, 1.0], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getMarginal(1).getRealization())
[0.608202]
>>> print(randomVector.getMarginal(1).getDistribution())
Normal(mu = 0, sigma = 1)
getMean(self)

Accessor to the mean of the RandomVector.

Returns
meanPoint

Mean of the considered UsualRandomVector.

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.5], [1.0, 1.5], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getMean())
[0,0.5]
getName(self)

Accessor to the object’s name.

Returns
namestr

The name of the object.

getOperator(self)

Accessor to the comparaison operator of the Event.

Returns
operatorComparisonOperator

Comparaison operator used to define the RandomVector.

getParameter(self)

Accessor to the parameter of the distribution.

Returns
parameterPoint

Parameter values.

getParameterDescription(self)

Accessor to the parameter description of the distribution.

Returns
descriptionDescription

Parameter names.

getRealization(self)

Compute one realization of the RandomVector.

Returns
aRealizationPoint

Sequence of values randomly determined from the RandomVector definition. In the case of an event: one realization of the event (considered as a Bernoulli variable) which is a boolean value (1 for the realization of the event and 0 else).

See also

getSample

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.0], [1.0, 1.0], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getRealization())
[0.608202,-1.26617]
>>> print(randomVector.getRealization())
[-0.438266,1.20548]
getSample(self, size)

Compute realizations of the RandomVector.

Parameters
nint,

Number of realizations needed.

Returns
realizationsSample

n sequences of values randomly determined from the RandomVector definition. In the case of an event: n realizations of the event (considered as a Bernoulli variable) which are boolean values (1 for the realization of the event and 0 else).

See also

getRealization

Examples

>>> import openturns as ot
>>> distribution = ot.Normal([0.0, 0.0], [1.0, 1.0], ot.CorrelationMatrix(2))
>>> randomVector = ot.RandomVector(distribution)
>>> ot.RandomGenerator.SetSeed(0)
>>> print(randomVector.getSample(3))
[ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
getThreshold(self)

Accessor to the threshold of the Event.

Returns
thresholdfloat

Threshold of the RandomVector.

intersect(self, other)

Intersection of two events.

Parameters
eventRandomVector

A composite event

Returns
eventRandomVector

Intersection event

isComposite(self)

Accessor to know if the RandomVector is a composite one.

Returns
isCompositebool

Indicates if the RandomVector is of type Composite or not.

isEvent(self)

Whether the random vector is an event.

Returns
isEventbool

Whether it takes it values in {0, 1}.

join(self, other)

Union of two events.

Parameters
eventRandomVector

A composite event

Returns
eventRandomVector

Union event

setDescription(self, description)

Accessor to the description of the RandomVector.

Parameters
descriptionstr or sequence of str

Describes the components of the RandomVector.

setName(self, name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setParameter(self, parameters)

Accessor to the parameter of the distribution.

Parameters
parametersequence of float

Parameter values.