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"""
Distribution manipulation
=========================
"""
# %%
# In this example we are going to exhibit some of the services exposed by the distribution objects:
#
# - ask for the dimension, with the method `getDimension` ;
# - extract the marginal distributions, with the method `getMarginal` ;
# - to ask for some properties, with `isContinuous`, `isDiscrete`, `isElliptical` ;
# - to get the copula, with the method `getCopula` ;
# - to ask for some properties on the copula, with the methods `hasIndependentCopula`, `hasEllipticalCopula` ;
# - to evaluate some moments, with `getMean`, `getStandardDeviation`, `getCovariance`, `getSkewness`, `getKurtosis` ;
# - to evaluate the roughness, with the method `getRoughness` ;
# - to get one realization or simultaneously :math:`n` realizations, with the method `getRealization`, `getSample` ;
# - to evaluate the probability content of a given interval, with the method `computeProbability` ;
# - to evaluate a quantile or a complementary quantile, with the method `computeQuantile` ;
# - to evaluate the characteristic function of the distribution ;
# - to evaluate the derivative of the CDF or PDF ;
# - to draw some curves.
# %%
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)
# %%
# Create an 1-d distribution
dist_1 = ot.Normal()
# Create a 2-d distribution
dist_2 = ot.JointDistribution(
[ot.Normal(), ot.Triangular(0.0, 2.0, 3.0)], ot.ClaytonCopula(2.3)
)
# Create a 3-d distribution
copula_dim3 = ot.Student(5.0, 3).getCopula()
dist_3 = ot.JointDistribution(
[ot.Normal(), ot.Triangular(0.0, 2.0, 3.0), ot.Exponential(0.2)], copula_dim3
)
# %%
# Get the dimension fo the distribution
dist_2.getDimension()
# %%
# Get the 2nd marginal
dist_2.getMarginal(1)
# %%
# Get a 2-d marginal
dist_3.getMarginal([0, 1]).getDimension()
# %%
# Ask some properties of the distribution
dist_1.isContinuous(), dist_1.isDiscrete(), dist_1.isElliptical()
# %%
# Get the copula
copula = dist_2.getCopula()
# %%
# Ask some properties on the copula
dist_2.hasIndependentCopula(), dist_2.hasEllipticalCopula()
# %%
# Get the mean vector of the distribution
dist_2.getMean()
# %%
# Get the standard deviation vector of the distribution
dist_2.getStandardDeviation()
# %%
# Get the covariance matrix of the distribution
dist_2.getCovariance()
# %%
# Get the skewness vector of the distribution
dist_2.getSkewness()
# %%
# Get the kurtosis vector of the distribution
dist_2.getKurtosis()
# %%
# Get the roughness of the distribution
dist_1.getRoughness()
# %%
# Get one realization
dist_2.getRealization()
# %%
# Get several realizations
dist_2.getSample(5)
# %%
# Evaluate the PDF at the mean point
dist_2.computePDF(dist_2.getMean())
# %%
# Evaluate the CDF at the mean point
dist_2.computeCDF(dist_2.getMean())
# %%
# Evaluate the complementary CDF
dist_2.computeComplementaryCDF(dist_2.getMean())
# %%
# Evaluate the survival function at the mean point
dist_2.computeSurvivalFunction(dist_2.getMean())
# %%
# Evaluate the PDF on a sample
dist_2.computePDF(dist_2.getSample(5))
# %%
# Evaluate the CDF on a sample
dist_2.computeCDF(dist_2.getSample(5))
# %%
# Evaluate the probability content of an 1-d interval
interval = ot.Interval(-2.0, 3.0)
dist_1.computeProbability(interval)
# %%
# Evaluate the probability content of a 2-d interval
interval = ot.Interval([0.4, -1], [3.4, 2])
dist_2.computeProbability(interval)
# %%
# Evaluate the quantile of order `p=90%`
dist_2.computeQuantile(0.90)
# %%
# and the quantile of order 1-p
dist_2.computeQuantile(0.90, True)
# %%
# Evaluate the quantiles of order p et q
# For example, the quantile `90%` and `95%`
dist_1.computeQuantile([0.90, 0.95])
# %%
# and the quantile of order 1-p and 1-q
dist_1.computeQuantile([0.90, 0.95], True)
# %%
# Evaluate the characteristic function of the distribution (only 1-d)
dist_1.computeCharacteristicFunction(dist_1.getMean()[0])
# %%
# Evaluate the derivatives of the PDF with respect to the parameters at mean
dist_2.computePDFGradient(dist_2.getMean())
# %%
# Evaluate the derivatives of the CDF with respect to the parameters at mean
dist_2.computeCDFGradient(dist_2.getMean())
# %%
# Draw PDF
graph = dist_1.drawPDF()
view = viewer.View(graph)
# %%
# Draw CDF
graph = dist_1.drawCDF()
view = viewer.View(graph)
# %%
# Draw an 1-d quantile curve
# Define the range and the number of points
qMin = 0.2
qMax = 0.6
nbrPoints = 101
quantileGraph = dist_1.drawQuantile(qMin, qMax, nbrPoints)
view = viewer.View(quantileGraph)
# %%
# Draw a 2-d quantile curve
# Define the range and the number of points
qMin = 0.3
qMax = 0.9
nbrPoints = 101
quantileGraph = dist_2.drawQuantile(qMin, qMax, nbrPoints)
view = viewer.View(quantileGraph)
plt.show()
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