Estimate moments from sample

In this example we are going to estimate statistical moments from a sample, eventually from an output variable of interest.

from __future__ import print_function
import openturns as ot
ot.Log.Show(ot.Log.NONE)

Create a sample

# model f
model = ot.SymbolicFunction(["x1", "x2"], ["x1^2+x2", "x2^2+x1"])

# input vector X
inputDist = ot.ComposedDistribution([ot.Normal()] * 2, ot.IndependentCopula(2))
inputDist.setDescription(['X1', 'X2'])
inputVector = ot.RandomVector(inputDist)

# output vector Y=f(X)
output = ot.CompositeRandomVector(model, inputVector)

# sample Y
size = 1000
sample = output.getSample(size)

Estimate mean

sample.computeMean()

[0.923615,1.02297]

Estimate standard deviation

sample.computeStandardDeviation()

[[ 1.65759 0 ]
[ 0.0710817 1.81269 ]]

Estimate variance

sample.computeVariance()

[2.74761,3.2909]

Estimate skewness

sample.computeSkewness()

[1.44617,1.73649]

Estimate kurtosis

sample.computeKurtosis()

[7.00125,8.00153]