Create a truncated distributionΒΆ

In this example we are going to define truncated distributions.

It is possible to truncate a distribution in its lower area, or its upper area or in both lower and upper areas.

In 1-d, assuming a and b bounds, its probability density function is defined as:

\forall y \in \mathbb{R}, p_Y(y) = \begin{array}{|ll} 0 & \mbox{for } y \geq b \mbox{ or } y \leq a\\ \displaystyle \frac{1}{F_X(b) - F_X(a)}\, p_X(y) & \mbox{for } y\in[a,b] \end{array}

Is is also possible to truncate a multivariate distribution.

[1]:

from __future__ import print_function
import openturns as ot

# the original distribution
distribution = ot.Gumbel(0.45, 0.6)
distribution.drawPDF()

[1]:
../../_images/examples_probabilistic_modeling_truncated_distribution_2_0.svg
[2]:

# truncate on the left
truncated = ot.TruncatedDistribution(distribution, 0.2, ot.TruncatedDistribution.LOWER)
truncated.drawPDF()

[2]:
../../_images/examples_probabilistic_modeling_truncated_distribution_3_0.svg
[3]:

# truncate on the right
truncated = ot.TruncatedDistribution(distribution, 1.5, ot.TruncatedDistribution.UPPER)
truncated.drawPDF()

[3]:
../../_images/examples_probabilistic_modeling_truncated_distribution_4_0.svg
[4]:

# truncated on both bounds
truncated = ot.TruncatedDistribution(distribution, 0.2, 1.5)
truncated.drawPDF()

[4]:
../../_images/examples_probabilistic_modeling_truncated_distribution_5_0.svg
[5]:

# Define a multivariate distribution
dimension = 2
size = 70
sample = ot.Normal(dimension).getSample(size)
ks = ot.KernelSmoothing().build(sample)

[6]:

# Truncate it between (-2;2)^n
bounds = ot.Interval([-2.0] * dimension, [2.0] * dimension)
truncatedKS = ot.Distribution(ot.TruncatedDistribution(ks, bounds))

[7]:

# Draw its PDF
graph = truncatedKS.drawPDF([-2.5] * dimension, [2.5] * dimension, [256] * dimension)
graph.add(ot.Cloud(truncatedKS.getSample(200)))
graph.setColors(["blue", "red"])
graph

[7]:
../../_images/examples_probabilistic_modeling_truncated_distribution_8_0.svg