Create a composed distribution

In this example we are going to create a multidimensional distribution described by its marginal distributions and optionally its dependence structure (a particular copula).

from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)

create the marginals

marginals = [ot.Normal(), ot.Gumbel()]

create the multivariate distribution, assume no dependency structure

distribution = ot.ComposedDistribution(marginals)

draw PDF

graph = distribution.drawPDF()
view = viewer.View(graph)

create the copula which specifies the dependency structure

R = ot.CorrelationMatrix(2)
R[0, 1] = 0.3
copula = ot.NormalCopula(R)
copula

NormalCopula(R = [[ 1 0.3 ]
[ 0.3 1 ]])

create the multivariate distribution with the desired copula

distribution = ot.ComposedDistribution(marginals, copula)

draw PDF

graph = distribution.drawPDF()
view = viewer.View(graph)
plt.show()