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.

$Y = \sum_{i=1}^{20} X_i$

where

$X_i \tilde{} U(1,2,3,4,5,6)$

[13]:

from __future__ import print_function
import openturns as ot

[14]:

# create the distribution associated to the dice roll
X = ot.UserDefined([[i] for i in range(1,7)])

[23]:

# Roll the dice a few times
X.getSample(10)

[23]:

[16]:

N = 20

[17]:

# Create the collection of identically distributed Xi
coll = [X] * N

[18]:

# Create the weights
weight = [1.0] * N

[19]:

# create the affine combination
distribution = ot.RandomMixture(coll, weight)

[20]:

# probability to exceed a sum of 100 after 20 dice rolls
distribution.computeComplementaryCDF(100)

[20]:

1.576207331110968e-05

[21]:

# draw PDF
distribution.drawPDF()

[21]:

[22]:

# draw CDF
distribution.drawCDF()

[22]:

OpenTURNS