Probability distributions based on OpenTURNS

In this example, we seek to create a probability distribution based on the OpenTURNS library.

from __future__ import annotations

from gemseo import configure_logger
from gemseo.uncertainty import create_distribution
from gemseo.uncertainty import get_available_distributions

configure_logger()

<RootLogger root (INFO)>

First of all, we can access the names of the available probability distributions from the API:

all_distributions = get_available_distributions()
all_distributions

['OTBetaDistribution', 'OTDiracDistribution', 'OTDistribution', 'OTExponentialDistribution', 'OTJointDistribution', 'OTLogNormalDistribution', 'OTNormalDistribution', 'OTTriangularDistribution', 'OTUniformDistribution', 'OTWeibullDistribution', 'SPBetaDistribution', 'SPDistribution', 'SPExponentialDistribution', 'SPJointDistribution', 'SPLogNormalDistribution', 'SPNormalDistribution', 'SPTriangularDistribution', 'SPUniformDistribution', 'SPWeibullDistribution']

and filter the ones based on the OpenTURNS library (their names start with the acronym 'OT'):

ot_distributions = get_available_distributions("OTDistribution")
ot_distributions

['OTBetaDistribution', 'OTDiracDistribution', 'OTDistribution', 'OTExponentialDistribution', 'OTLogNormalDistribution', 'OTNormalDistribution', 'OTTriangularDistribution', 'OTUniformDistribution', 'OTWeibullDistribution']

Create a distribution

Then, we can create a probability distribution, e.g. a normal distribution.

Case 1: the OpenTURNS distribution has a GEMSEO class

For the standard normal distribution (mean = 0 and standard deviation = 1):

distribution_0_1 = create_distribution("OTNormalDistribution")
distribution_0_1

Normal(mu=0.0, sigma=1.0)

For a normal with mean = 1 and standard deviation = 2:

distribution_1_2 = create_distribution("OTNormalDistribution", mu=1.0, sigma=2.0)
distribution_1_2

Normal(mu=1.0, sigma=2.0)

Case 2: the OpenTURNS distribution has no GEMSEO class

When GEMSEO does not offer a class for the OpenTURNS distribution, we can use the generic GEMSEO class OTDistribution to create any OpenTURNS distribution by setting interfaced_distribution to its OpenTURNS name and parameters as a tuple of OpenTURNS parameter values (see the documentation of OpenTURNS).

distribution_1_2 = create_distribution(
    "OTDistribution", interfaced_distribution="Normal", parameters=(1.0, 2.0)
)
distribution_1_2

Normal(1.0, 2.0)

Plot the distribution

We can plot both cumulative and probability density functions:

distribution_0_1.plot()

<Figure size 640x320 with 2 Axes>

Get statistics

Mean

We can access the mean of the distribution:

distribution_0_1.mean

0.0

Standard deviation

We can access the standard deviation of the distribution:

distribution_0_1.standard_deviation

1.0

Numerical range

We can access the range, i.e. the difference between the numerical minimum and maximum, of the distribution:

distribution_0_1.range

array([-7.65062809,  7.65062809])

Mathematical support

We can access the range, i.e. the difference between the minimum and maximum, of the distribution:

distribution_0_1.support

array([-inf,  inf])

Evaluate CDF

We can evaluate the cumulative density function:

distribution_0_1.compute_cdf(0.5)

0.6914624612740131

Evaluate inverse CDF

We can evaluate the inverse cumulative density function, here the quantile at 97.5%:

distribution_0_1.compute_inverse_cdf(0.975)

1.9599639845400538

Generate samples

We can generate 10 samples of the distribution:

distribution_0_1.compute_samples(10)

array([ 0.60820165, -1.2661731 , -0.43826562,  1.2054782 , -2.18138523,
        0.35004209, -0.35500705,  1.43724931,  0.81066798,  0.79315601])