Create a deconditioned distribution¶

In this example we are going to build the distribution of the random vector $\inputRV$ defined by the conditional distribution of:

$\inputRV|\vect{\Theta}$

where $\vect{\Theta}$ is the output of the random variable $\vect{Y}$ through the link function $f$ :

$\vect{\Theta} & = f(\vect{Y})\\ \vect{Y} & \sim \cL_{\vect{Y}}$

This example creates a DeconditionedDistribution which offers all the methods attached to the distributions.

We consider the case where $X$ is of dimension 1 and follows a uniform distribution defined by:

Variable	Distribution	Parameter
$X$	`Uniform` ( $a, b$ )	$(a,b) = (Y, 1+Y^2)$
$Y$	`Uniform` ( $c, d$ )	$(c,d) = (-1, 1)$

import openturns as ot
import openturns.viewer as otv

Create the $Y$ distribution.

YDist = ot.Uniform(-1.0, 1.0)

Create the link function $f: y \rightarrow (y, 1+y^2)$ .

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

Create the conditional distribution of $\vect{X}|\vect{\Theta}$ : as the parameters have no importance, we use the default distribution.

XgivenThetaDist = ot.Uniform()

Create the deconditioned distribution of $X$ .

XDist = ot.DeconditionedDistribution(XgivenThetaDist, YDist, f)
XDist.setDescription([r"$X|\mathbf{\boldsymbol{\Theta}} = f(Y)$"])
XDist

DeconditionedDistribution

Get a sample:

XDist.getSample(5)

Draw the PDF.

graph = XDist.drawPDF()
view = otv.View(graph)

view.ShowAll()

OpenTURNS