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Fit a distribution from an input sample¶
In this example we show how to use the
BuildDistribution()
function to fit a distribution to an
input sample.
This function is used by the FunctionalChaosAlgorithm
class when we want to create a polynomial chaos metamodel and we have a
design of experiments which have been computed beforehand.
In this case, we have to identify the distributions which best fit to the
input sample in order to define the input probabilistic model.
This is, in turn, used by in the polynomial chaos to create the orthogonal basis.
import openturns as ot
ot.Log.Show(ot.Log.NONE)
We first create the function model.
ot.RandomGenerator.SetSeed(0)
dimension = 2
input_names = ["x1", "x2"]
formulas = ["cos(x1 + x2)", "(x2 + 1) * exp(x1)"]
model = ot.SymbolicFunction(input_names, formulas)
Then we create a sample x and compute the corresponding output sample y.
distribution = ot.Normal(dimension)
samplesize = 1000
inputSample = distribution.getSample(samplesize)
outputSample = model(inputSample)
Create a functional chaos model.
The algorithm used by BuildDistribution()
fits a distribution on the input sample.
This is done with the Lilliefors test.
Please read Kolmogorov-Smirnov fitting test for more details on this topic.
The Lilliefors test is based on sampling the distribution of the
Kolmogorov-Smirnov statistics.
The sample size corresponding to this algorithm is configured
by the “FittingTest-LillieforsMaximumSamplingSize” ResourceMap
key.
In order to get satisfactory results, the default value of this
key is relatively large.
ot.ResourceMap.GetAsUnsignedInteger("FittingTest-LillieforsMaximumSamplingSize")
100000
In order to speed this example up, let us reduce this value.
ot.ResourceMap.SetAsUnsignedInteger("FittingTest-LillieforsMaximumSamplingSize", 100)
Then we fit the distribution.
distribution = ot.FunctionalChaosAlgorithm.BuildDistribution(inputSample)
Let us explore the distribution with its fitted parameters.
distribution
We can also analyse its properties in more detail.
for i in range(dimension):
marginal = distribution.getMarginal(i)
marginalname = marginal.getImplementation().getClassName()
print("Marginal #", i, ":", marginalname)
distribution.getCopula()
Marginal # 0 : Normal
Marginal # 1 : Normal
The previous call to BuildDistribution()
is what is done internally by the
following constructor of FunctionalChaosAlgorithm.
algo = ot.FunctionalChaosAlgorithm(inputSample, outputSample)
The previous constructor is the main topic of the example Create a polynomial chaos metamodel from a data set.
ot.ResourceMap.Reload() # reset default settings
Total running time of the script: (0 minutes 2.122 seconds)