Create a discrete random mixture

In this example we are going to build the distribution of the value of the sum of 20 dice rolls.

where

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 distribution associated to the dice roll

X = ot.UserDefined([[i] for i in range(1,7)])

Roll the dice a few times

X.getSample(10)

	v0
0	1
1	3
2	6
3	1
4	6
5	3
6	2
7	2
8	4
9	2

N = 20

Create the collection of identically distributed Xi

coll = [X] * N

Create the weights

weight = [1.0] * N

create the affine combination

distribution = ot.RandomMixture(coll, weight)

probability to exceed a sum of 100 after 20 dice rolls

distribution.computeComplementaryCDF(100)

Out:

1.576207331110968e-05

draw PDF

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

draw CDF

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