Create a conditional distribution¶

In this example we are going to build the distribution of the random vector $\vect{X}$ conditioned by the random vector $\vect{\Theta}$

$\vect{X}|\vect{\Theta}$

with $\vect{\Theta}$ obtained with the random variable $Y$ through a function $f$

$\vect{\Theta}=f(Y)$

import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt

Create the $Y$ distribution

YDist = ot.Uniform(-1.0, 1.0)

Create $\vect{\Theta}=f(Y)$

f = ot.SymbolicFunction(["y"], ["y", "1+y^2"])

Create the $\vect{X}|\vect{\Theta}$ distribution

XgivenThetaDist = ot.Uniform()

create the distribution

XDist = ot.DeconditionedDistribution(XgivenThetaDist, YDist, f)
XDist.setDescription(["X|Theta=f(y)"])
XDist

DeconditionedDistribution

Get a sample

XDist.getSample(5)

Draw PDF

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

OpenTURNS