Create a random vector

The RandomVector object represents the concept of random variable.

This class can be cerated by:

• Case 1: directly using the RandomVector class,

• Case 2: from python, using the PythonRandomVector class which enables to redefine some methods (as the sampling method for example).

import openturns as ot

Case 1: use the RandomVector class

We create the random vector following the Normal distribution with zero mean and unit variance.

dist3d = ot.Normal(3)
X = ot.RandomVector(dist3d)

Get the dimension

X.getDimension()

3

Get the mean

X.getMean()

class=Point name=Unnamed dimension=3 values=[0,0,0]

Get the covariance

X.getCovariance()

[[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 1 ]]

Draw a sample

X.getSample(5)

	X0	X1	X2
0	0.6082017	-1.266173	-0.4382656
1	1.205478	-2.181385	0.3500421
2	-0.355007	1.437249	0.810668
3	0.793156	-0.4705256	0.2610179
4	-2.290062	-1.282885	-1.311781

Extract the component :

X1 = X.getMarginal(1)
X1.getSample(5)

	X1
0	-0.09078383
1	0.9957932
2	-0.1394528
3	-0.5602056
4	0.4454897

Extract the component .

X02 = X.getMarginal([0, 2])
X02.getSample(5)

	X0	X2
0	0.322925	0.4457853
1	-1.038077	-0.8567123
2	0.4736169	-0.1254977
3	0.3514178	1.782359
4	0.07020736	-0.7813665

Case 2: use the PythonRandomVector class

We create a random vector using the PythonRandomVector class, which enables to overload the following methods: getRealization, getSample, getMean and getCovariance.

Inherit PythonRandomVector Here, we create a random vector of dimension 2 , where and with independent components.

class RVEC(ot.PythonRandomVector):
    def __init__(self):
        super(RVEC, self).__init__(2)
        self.setDescription(["R", "S"])

    def getRealization(self):
        X = [ot.RandomGenerator.Generate(), 2.0 + ot.RandomGenerator.Generate()]
        return X

    def getSample(self, size):
        X = []
        for i in range(size):
            X.append(
                [ot.RandomGenerator.Generate(), 2.0 + ot.RandomGenerator.Generate()]
            )
        return X

    def getMean(self):
        return [0.5, 2.5]

    def getCovariance(self):
        return [[1.0 / 12.0, 0.0], [0.0, 1.0 / 12.0]]

Instantiate the distribution

randomVector = ot.RandomVector(RVEC())

Get a sample

randomVector.getSample(5)

	v0	v1
0	0.2036527	2.855795
1	0.4350783	2.361664
2	0.002107615	2.239434
3	0.2551563	2.591534
4	0.1692165	2.977334

Get its mean

randomVector.getMean()

class=Point name=Unnamed dimension=2 values=[0.5,2.5]

Compute the probability contained in an interval

randomVector.getCovariance()

[[ 0.0833333 0 ]
[ 0 0.0833333 ]]