12.1. Tests based on the Empirical Distribution Function (“EDF tests”)

The implemented tests are the Kolmogorov-Smirnov (\(D\)) test, the Cramer-VonMises (\(W^2\)) test and the Anderson-Darling (\(A^2\)) test. Their aim is to compare a given attribute to a bunch of implemented laws among the following list: the normal, lognormal and uniform law. The details of the computation is given in [Bla17]. The following piece of code gives an example of what can be achieved using these three classes and the usage of their options defined in the summary block below. Figure 12.1 shows the results of such a script.

"""
Example of distribution testing with different quality criteria
"""
from URANIE import DataServer, Sampler, UncertModeler
import ROOT

# Create a TDS with 3 kind of distributions
tds0 = DataServer.TDataServer()
tds0.addAttribute(DataServer.TNormalDistribution("n", 1.3, 4.5))
tds0.addAttribute(DataServer.TLogNormalDistribution("ln", 1.3, 4.5))
tds0.addAttribute(DataServer.TUniformDistribution("u", -1.3, 4.5))

# Create the sample
fsamp = Sampler.TBasicSampling(tds0, "lhs", 1000)
fsamp.generateSample()

# Create the canvas
c = ROOT.TCanvas("c1", "", 5, 20, 1300, 600)
apad = ROOT.TPad("apad", "apad", 0, 0.03, 1, 1)
apad.Draw()
apad.cd()
apad.Divide(3)

apad.cd(1)
tks_n = UncertModeler.TTestKolmogorovSmirnov(tds0, "n")
tcvm_n = UncertModeler.TTestCramerVonMises(tds0, "n")
tad_n = UncertModeler.TTestAndersonDarling(tds0, "n")
# Test wrt to a normal distribution whose mu and sigma are taken from
# the original distribution
tks_n.computeScore("same:normal")
tad_n.computeScore("same:normal(0.8,4.5))")  # put wrong mu
tcvm_n.computeScore("same:normal(1.3,5.5)")  # put wrong sigma

apad.cd(2)
tks_ln = UncertModeler.TTestKolmogorovSmirnov(tds0, "ln")
tcvm_ln = UncertModeler.TTestCramerVonMises(tds0, "ln")
tad_ln = UncertModeler.TTestAndersonDarling(tds0, "ln")
# Test wrt to a lognormal distribution whose mu and sigma are taken from
# the original distribution
tks_ln.computeScore("same:lognormal")
tad_ln.computeScore("same:lognormal(1.2,4.5))")  # put wrong mu
tcvm_ln.computeScore("same:lognormal(1.3,3.5)")  # put wrong sigma

apad.cd(3)
tks_u = UncertModeler.TTestKolmogorovSmirnov(tds0, "u")
tcvm_u = UncertModeler.TTestCramerVonMises(tds0, "u")
tad_u = UncertModeler.TTestAndersonDarling(tds0, "u")
# Test wrt to an uniform distribution whose min and max are taken from
# the original distribution (and compared to a normal as well, for fun)
tks_u.computeScore("same:uniform")
tad_u.computeScore("same:uniform(-1.2,4.5)")  # put wrong min
tcvm_u.computeScore("same:uniform(-1.3,4.6)")  # put wrong max

Figure 12.1 Results of the macro defined previously to produce variety of test of already implemented distributions

Summary: Tests based on the EDF (TTestKolmogorovSmirnov, TTestCramerVonMises and TTestAndersonDarling classes)

• TTestKolmogorovSmirnov(TDataServer tds, const char * sAtt, Option_t * option=””)

  Define the Kolmogorov-Smirnov (D) test for the attribute sAtt. No option is used.

• TTestCramerVonMises(TDataServer tds, const char * sAtt, Option_t * option=””)

  Define the Cramer-VonMises (W2) test for the attribute sAtt. No option is used.

• TTestAndersonDarling(TDataServer tds, const char * sAtt, Option_t * option=””)

  Define the Anderson-Darling (A2) test for the attribute sAtt. No option is used.

• computeScore(Option_t* option=””)

  Compute the score for the current test ( D, W2 and A2) with laws defined in the option parameter. The laws are separated by the “:” character. If the parameters of the law are defined by the user, they are defined in brackets “()” as normal(30576,1450). If the parameters must be estimated by the algorithm, do not use the brackets as normal. Actually, the laws implemented are the normal and lognormal laws.