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()

[0.922865,1.02244]

Estimate standard deviation

sample.computeStandardDeviation()

[1.65359,1.8197]

Estimate variance

sample.computeVariance()

[2.73435,3.31132]

Estimate skewness

sample.computeSkewness()

[1.44932,1.72739]

Estimate kurtosis

sample.computeKurtosis()

[7.05724,7.92245]