Create a truncated distribution¶
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:
Is is also possible to truncate a multivariate distribution.
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) # the original distribution distribution = ot.Gumbel(0.45, 0.6) graph = distribution.drawPDF() view = viewer.View(graph)
truncate on the left
truncated = ot.TruncatedDistribution(distribution, 0.2, ot.TruncatedDistribution.LOWER) graph = truncated.drawPDF() view = viewer.View(graph)
truncate on the right
truncated = ot.TruncatedDistribution(distribution, 1.5, ot.TruncatedDistribution.UPPER) graph = truncated.drawPDF() view = viewer.View(graph)
truncated on both bounds
truncated = ot.TruncatedDistribution(distribution, 0.2, 1.5) graph = truncated.drawPDF() view = viewer.View(graph)
Define a multivariate distribution
dimension = 2 size = 70 sample = ot.Normal(dimension).getSample(size) ks = ot.KernelSmoothing().build(sample)
Truncate it between (-2;2)^n
bounds = ot.Interval([-2.0] * dimension, [2.0] * dimension) truncatedKS = ot.Distribution(ot.TruncatedDistribution(ks, bounds))
Draw its PDF
graph = truncatedKS.drawPDF([-2.5] * dimension, [2.5] * dimension,  * dimension) graph.add(ot.Cloud(truncatedKS.getSample(200))) graph.setColors(["blue", "red"]) view = viewer.View(graph) plt.show()
/home/devel/project/build/python/src/site-packages/openturns/viewer.py:432: UserWarning: No contour levels were found within the data range. contourset = self._ax.contour(X, Y, Z, **contour_kw)
Total running time of the script: ( 0 minutes 0.410 seconds)