Note

Click here to download the full example code

# 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:

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, [256] * dimension)
graph.add(ot.Cloud(truncatedKS.getSample(200)))
graph.setColors(["blue", "red"])
view = viewer.View(graph)
plt.show()
```

Out:

```
/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[0].contour(X, Y, Z, **contour_kw)
```

**Total running time of the script:** ( 0 minutes 0.410 seconds)