Create a composite distribution

In this example we are going to create a distribution defined as the push-forward distribution of a scalar distribution by a transformation.

If we note a scalar distribution, a mapping, then it is possible to create the push-forward distribution defined by

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 an 1-d distribution

antecedent = ot.Normal()

Create an 1-d transformation

f = ot.SymbolicFunction(['x'], ['sin(x)+cos(x)'])

Create the composite distribution

distribution = ot.CompositeDistribution(f, antecedent)
graph = distribution.drawPDF()
view = viewer.View(graph)

Using the simplified construction

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

Using chained operators

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