Note
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Sample manipulation¶
This example will describe the main statistical functionalities on data through the Sample object. The Sample is an output variable of interest.
import openturns as ot
ot.Log.Show(ot.Log.NONE)
A typical example¶
A recurring issue in uncertainty quantification is to perform analysis on an output variable of interest Y obtained through a model f and input parameters X. Here we shall consider the input parameters as two independent standard normal distributions . We therefore use an IndependentCopula to describe the link between the two marginals.
# input parameters
inputDist = ot.ComposedDistribution([ot.Normal()] * 2, ot.IndependentCopula(2))
inputDist.setDescription(["X1", "X2"])
We create a vector from the 2D-distribution created before :
inputVector = ot.RandomVector(inputDist)
Suppose our model f is known and reads as :
We define our model f with a SymbolicFunction
f = ot.SymbolicFunction(["x1", "x2"], ["x1^2+x2", "x2^2+x1"])
Our output vector is Y=f(X), the image of the inputVector by the model
outputVector = ot.CompositeRandomVector(f, inputVector)
We can now get a sample out of Y, that is realizations (here 1000) of the random outputVector
size = 1000
sample = outputVector.getSample(size)
The sample may be seen as a matrix of size . We print the 5 first samples (out of 1000) :
sample[:5]
Basic operations on samples¶
We have access to basic information about a sample such as
minimum and maximum per component
sample.getMin(), sample.getMax()
(class=Point name=Unnamed dimension=2 values=[-2.56587,-2.84726], class=Point name=Unnamed dimension=2 values=[9.93535,12.1777])
the range per component (max-min)
sample.computeRange()
More elaborate functionalities are also available :
get the median per component
sample.computeMedian()
compute the covariance
sample.computeCovariance()
get the empirical 0.95 quantile per component
sample.computeQuantilePerComponent(0.95)
get the value of the empirical CDF at a point
point = [1.1, 2.2]
sample.computeEmpiricalCDF(point)
0.517
Estimate the statistical moments¶
Oftentimes, we need to estimate the first moments of the output data. We can then estimate statistical moments from the output sample :
estimate the moment of order 1 : mean
sample.computeMean()
estimate the standard deviation for each component
sample.computeStandardDeviation()
estimate the moment of order 2 : variance
sample.computeVariance()
estimate the moment of order 3 : skewness
sample.computeSkewness()
estimate the moment of order 4 : kurtosis
sample.computeKurtosis()
Test the correlation¶
Some statistical test for correlation are available :
get the sample Pearson correlation matrix :
sample.computePearsonCorrelation()
get the sample Kendall correlation matrix :
sample.computeKendallTau()
get the sample Spearman correlation matrix :
sample.computeSpearmanCorrelation()