GoFTest class implementing the 1 sample and 2 sample goodness of fit tests for uni-variate distributions and data.

The class implements the AndersonDarling and the KolmogorovSmirnov tests

In the case of the 1-sample test the user needs to provide:

input data
theoretical distribution. The distribution can be provided as a function object (functor) or an object implementing the ROOT::Math::IGenFunction interface. One can provide either the PDF (default) of the CDF (cumulative distribution) One can also provide a pre-defined function. In that case one needs to give also the distribution parameters otherwise the default values will be used. The pre-defined distributions are:
- kGaussian with default parameter mean=0, sigma=1
- kExponential with default parameter rate=1
- kLogNormal with default parameter meanlog=0, sigmalog=1
Note that one should not use data computed distribution parameters, otherwise the test will be biased. The 1-sample KS test using data computed quantities is called Lilliefors test (see https://en.wikipedia.org/wiki/Lilliefors_test)

Definition at line 65 of file GoFTest.h.

Public Types
enum	EDistribution { kUndefined , kUserDefined , kGaussian , kLogNormal , kExponential }
	H0 distributions for using only with 1-sample tests. More...

enum	ETestType { kAD , kAD2s , kKS , kKS2s }
	Goodness of Fit test types for using with the class's unary functions as a shorthand for the in-built methods. More...

enum	EUserDistribution { kCDF , kPDF }
	User input distribution option. More...

Public Member Functions
	GoFTest (size_t sample1Size, const Double_t sample1, size_t sample2Size, const Double_t sample2)
	Constructor for 2-samples tests.

	GoFTest (size_t sampleSize, const Double_t *sample, const IGenFunction &dist, EUserDistribution userDist=kPDF, Double_t xmin=1, Double_t xmax=0)
	Constructor for 1-sample tests with a user specified distribution implementing the ROOT::Math::IGenFunction interface.

template<class Dist >
	GoFTest (size_t sampleSize, const Double_t *sample, Dist &dist, EUserDistribution userDist=kPDF, Double_t xmin=1, Double_t xmax=0)
	Templated constructor for 1-sample tests with a user specified distribution as a functor object implementing `double operator()(double x)`.

	GoFTest (size_t sampleSize, const Double_t *sample, EDistribution dist=kUndefined, const std::vector< double > &distParams={})
	Constructor for 1-sample tests with a specified distribution.

virtual	~GoFTest ()

Double_t	AndersonDarling2SamplesTest (const Char_t *option="p") const
	Anderson-Darling 2-Sample Test.

void	AndersonDarling2SamplesTest (Double_t &pvalue, Double_t &testStat) const
	Performs the Anderson-Darling 2-Sample Test.

Double_t	AndersonDarlingTest (const Char_t *option="p") const
	Anderson-Darling 2-Sample Test.

void	AndersonDarlingTest (Double_t &pvalue, Double_t &testStat) const
	Performs the Anderson-Darling 1-Sample Test.

Double_t	KolmogorovSmirnov2SamplesTest (const Char_t *option="p") const
	Kolmogorov-Smirnov 2-Samples Test.

void	KolmogorovSmirnov2SamplesTest (Double_t &pvalue, Double_t &testStat) const
	Kolmogorov-Smirnov 2-Samples Test.

Double_t	KolmogorovSmirnovTest (const Char_t *option="p") const
	Kolmogorov-Smirnov 1-Sample Test.

void	KolmogorovSmirnovTest (Double_t &pvalue, Double_t &testStat) const
	Kolmogorov-Smirnov 1-Sample Test.

void	operator() (ETestType test, Double_t &pvalue, Double_t &testStat) const
	The class's unary functions performing the gif test according to the ETestType provided.

Double_t	operator() (ETestType test=kAD, const Char_t *option="p") const
	Returns default Anderson Darling 1-Sample Test and default p-value; option "t" returns the test statistic value specific to the test type.

void	SetDistribution (EDistribution dist, const std::vector< double > &distParams={})
	Sets the distribution for the predefined distribution types and optionally its parameters for 1-sample tests.

void	SetUserCDF (const IGenFunction &cdf, Double_t xmin=1, Double_t xmax=0)
	Specialization to set the user input distribution as a cumulative distribution function for 1-sample tests.

template<class Dist >
void	SetUserCDF (Dist &cdf, Double_t xmin=1, Double_t xmax=0)
	Sets the user input distribution as a cumulative distribution function for 1-sample tests.

void	SetUserDistribution (const IGenFunction &dist, GoFTest::EUserDistribution userDist=kPDF, Double_t xmin=1, Double_t xmax=0)
	Sets the user input distribution function for 1-sample test using the ROOT::Math::IGenFunction interface.

template<class Dist >
void	SetUserDistribution (Dist &dist, EUserDistribution userDist=kPDF, Double_t xmin=1, Double_t xmax=0)
	Sets the user input distribution function for 1-sample test as a generic functor object.

void	SetUserPDF (const IGenFunction &pdf, Double_t xmin=1, Double_t xmax=0)
	Specialization to set the user input distribution as a probability density function for 1-sample tests using the ROOT::Math::IGenFunction interface.

template<class Dist >
void	SetUserPDF (Dist &pdf, Double_t xmin=1, Double_t xmax=0)
	Sets the user input distribution as a probability density function for 1-sample tests.

Static Public Member Functions
static void	AndersonDarling2SamplesTest (const ROOT::Fit::BinData &data1, const ROOT::Fit::BinData &data2, Double_t &pvalue, Double_t &testStat)
	Compute the 2-Sample Anderson Darling test for binned data assuming equal data are present at the bin center values.

static Double_t	PValueADKSamples (size_t nsamples, Double_t A2)
	Computation of the K-Sample Anderson-Darling Test's p-value as described in (1)

Private Member Functions
	GoFTest ()
	Disallowed default constructor.

	GoFTest (GoFTest &gof)
	Disallowed copy constructor.

Double_t	ExponentialCDF (Double_t x) const

Double_t	GaussianCDF (Double_t x) const

void	Instantiate (const Double_t *sample, size_t sampleSize)

Double_t	LogNormalCDF (Double_t x) const

void	LogSample ()
	Applies the logarithm to the sample when the specified distribution to test is LogNormal.

GoFTest	operator= (GoFTest &gof)
	Disallowed assign operator.

Double_t	PValueAD1Sample (Double_t A2) const
	Computation of the 1-Sample Anderson-Darling Test's p-value.

void	SetCDF ()

void	SetDistributionFunction (const IGenFunction &cdf, Bool_t isPDF, Double_t xmin, Double_t xmax)

void	SetParameters (const std::vector< double > &params)
	Sets the distribution parameters.

void	SetSamples (std::vector< const Double_t * > samples, const std::vector< size_t > samplesSizes)
	set a vector of samples

Static Private Member Functions
static Double_t	GetSigmaN (const std::vector< size_t > &ns, size_t N)
	Computation of sigma_N as described in (1)

static Double_t	InterpolatePValues (int nsamples, Double_t A2)
	Linear interpolation used in GoFTest::PValueAD2Samples.

Private Attributes
std::unique_ptr< IGenFunction >	fCDF
	Pointer to CDF used in 1-sample test.

std::vector< Double_t >	fCombinedSamples
	The combined data.

EDistribution	fDist
	Type of distribution.

std::vector< Double_t >	fParams
	The distribution parameters (e.g. fParams[0] = mean, fParams[1] = sigma for a Gaussian)

std::vector< std::vector< Double_t > >	fSamples
	The input data.

Bool_t	fTestSampleFromH0

#include <Math/GoFTest.h>

Member Enumeration Documentation

◆ EDistribution

enum ROOT::Math::GoFTest::EDistribution

H0 distributions for using only with 1-sample tests.

One should provide the distribution parameters otherwise the default values will be used

Enumerator
kUndefined
kUserDefined	Default value for non templated 1-sample test. Set with SetDistribution.
kGaussian	For internal use only within the class's template constructor.
kLogNormal	Gaussian distribution with default mean=0, sigma=1.
kExponential	Lognormal distribution with default meanlog=0, sigmalog=1. Exponential distribution with default rate=1

Definition at line 70 of file GoFTest.h.

◆ ETestType

enum ROOT::Math::GoFTest::ETestType

Goodness of Fit test types for using with the class's unary functions as a shorthand for the in-built methods.

Enumerator
kAD
kAD2s	Anderson-Darling Test. Default value.
kKS	Anderson-Darling 2-Samples Test.
kKS2s	Kolmogorov-Smirnov Test. Kolmogorov-Smirnov 2-Samples Test

Definition at line 85 of file GoFTest.h.

◆ EUserDistribution

enum ROOT::Math::GoFTest::EUserDistribution

User input distribution option.

Enumerator

kCDF

kPDF

Input distribution is a CDF : cumulative distribution function.

Input distribution is a PDF (Default value)

Definition at line 79 of file GoFTest.h.

Constructor & Destructor Documentation

◆ GoFTest() [1/6]

ROOT::Math::GoFTest::GoFTest	(	size_t	sample1Size,
		const Double_t *	sample1,
		size_t	sample2Size,
		const Double_t *	sample2 )

Constructor for 2-samples tests.

Definition at line 134 of file GoFTest.cxx.

◆ GoFTest() [2/6]

ROOT::Math::GoFTest::GoFTest	(	size_t	sampleSize,
		const Double_t *	sample,
		EDistribution	dist = kUndefined,
		const std::vector< double > &	distParams = {} )

Constructor for 1-sample tests with a specified distribution.

If a specific distribution is not specified it can be set later using SetDistribution.

Definition at line 161 of file GoFTest.cxx.

◆ GoFTest() [3/6]

template<class Dist >

ROOT::Math::GoFTest::GoFTest	(	size_t	sampleSize,
		const Double_t *	sample,
		Dist &	dist,
		EUserDistribution	userDist = kPDF,
		Double_t	xmin = 1,
		Double_t	xmax = 0 )

inline

Templated constructor for 1-sample tests with a user specified distribution as a functor object implementing double operator()(double x).

Definition at line 101 of file GoFTest.h.

◆ GoFTest() [4/6]

ROOT::Math::GoFTest::GoFTest	(	size_t	sampleSize,
		const Double_t *	sample,
		const IGenFunction &	dist,
		EUserDistribution	userDist = kPDF,
		Double_t	xmin = 1,
		Double_t	xmax = 0 )

inline

Constructor for 1-sample tests with a user specified distribution implementing the ROOT::Math::IGenFunction interface.

Definition at line 109 of file GoFTest.h.

◆ ~GoFTest()

ROOT::Math::GoFTest::~GoFTest ( )

virtual

Definition at line 179 of file GoFTest.cxx.

◆ GoFTest() [5/6]

ROOT::Math::GoFTest::GoFTest ( )

private

Disallowed default constructor.

◆ GoFTest() [6/6]

ROOT::Math::GoFTest::GoFTest ( GoFTest & gof )

private

Disallowed copy constructor.

Member Function Documentation

◆ AndersonDarling2SamplesTest() [1/3]

Double_t ROOT::Math::GoFTest::AndersonDarling2SamplesTest ( const Char_t * option = "p" ) const

Anderson-Darling 2-Sample Test.

Returns by default the p-value; when using option "t" returns the test statistic value "A2".

Definition at line 854 of file GoFTest.cxx.

◆ AndersonDarling2SamplesTest() [2/3]

void ROOT::Math::GoFTest::AndersonDarling2SamplesTest	(	const ROOT::Fit::BinData &	data1,
		const ROOT::Fit::BinData &	data2,
		Double_t &	pvalue,
		Double_t &	testStat )

static

Compute the 2-Sample Anderson Darling test for binned data assuming equal data are present at the bin center values.

Used by TH1::AndersonDarling

Definition at line 750 of file GoFTest.cxx.

◆ AndersonDarling2SamplesTest() [3/3]

void ROOT::Math::GoFTest::AndersonDarling2SamplesTest	(	Double_t &	pvalue,
		Double_t &	testStat ) const

Performs the Anderson-Darling 2-Sample Test.

The Anderson-Darling K-Sample Test algorithm is described and taken from http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/andeksam.htm and from (1) Scholz F.W., Stephens M.A. (1987), K-sample Anderson-Darling Tests, Journal of the American Statistical Association, 82, 918–924. (2-samples variant implemented).

Definition at line 646 of file GoFTest.cxx.

◆ AndersonDarlingTest() [1/2]

Double_t ROOT::Math::GoFTest::AndersonDarlingTest ( const Char_t * option = "p" ) const

Anderson-Darling 2-Sample Test.

Returns default p-value; option "t" returns the test statistic value "A2"

Definition at line 890 of file GoFTest.cxx.

◆ AndersonDarlingTest() [2/2]

void ROOT::Math::GoFTest::AndersonDarlingTest	(	Double_t &	pvalue,
		Double_t &	testStat ) const

Performs the Anderson-Darling 1-Sample Test.

The Anderson-Darling 1-Sample Test algorithm for a specific distribution is described at http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/andedarl.htm and described and taken from (2) Marsaglia J.C.W., Marsaglia G. (2004), Evaluating the Anderson-Darling Distribution, Journal of Statistical Software, Volume 09, Issue i02. and described and taken from (3) Lewis P.A.W. (1961), The Annals of Mathematical Statistics, Distribution of the Anderson-Darling Statistic, Volume 32, Number 4, 1118-1124.

Definition at line 862 of file GoFTest.cxx.

◆ ExponentialCDF()

Double_t ROOT::Math::GoFTest::ExponentialCDF ( Double_t x ) const

private

Definition at line 299 of file GoFTest.cxx.

◆ GaussianCDF()

Double_t ROOT::Math::GoFTest::GaussianCDF ( Double_t x ) const

private

Definition at line 295 of file GoFTest.cxx.

◆ GetSigmaN()

Double_t ROOT::Math::GoFTest::GetSigmaN	(	const std::vector< size_t > &	ns,
		size_t	N )

staticprivate

Computation of sigma_N as described in (1)

Definition at line 311 of file GoFTest.cxx.

◆ Instantiate()

void ROOT::Math::GoFTest::Instantiate	(	const Double_t *	sample,
		size_t	sampleSize )

private

Definition at line 279 of file GoFTest.cxx.

◆ InterpolatePValues()

static Double_t ROOT::Math::GoFTest::InterpolatePValues	(	int	nsamples,
		Double_t	A2 )

staticprivate

Linear interpolation used in GoFTest::PValueAD2Samples.

◆ KolmogorovSmirnov2SamplesTest() [1/2]

Double_t ROOT::Math::GoFTest::KolmogorovSmirnov2SamplesTest ( const Char_t * option = "p" ) const

Kolmogorov-Smirnov 2-Samples Test.

Returns by default the p-value; option "t" returns the test statistic value "Dn".

Definition at line 913 of file GoFTest.cxx.

◆ KolmogorovSmirnov2SamplesTest() [2/2]

void ROOT::Math::GoFTest::KolmogorovSmirnov2SamplesTest	(	Double_t &	pvalue,
		Double_t &	testStat ) const

Kolmogorov-Smirnov 2-Samples Test.

The Kolmogorov-Smirnov 2-Samples Test algorithm is described at http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/ks2samp.htm and described and taken from http://root.cern.ch/root/html/TMath.html#TMath:KolmogorovTest

Definition at line 896 of file GoFTest.cxx.

◆ KolmogorovSmirnovTest() [1/2]

Double_t ROOT::Math::GoFTest::KolmogorovSmirnovTest ( const Char_t * option = "p" ) const

Kolmogorov-Smirnov 1-Sample Test.

Returns default p-value; option "t" returns the test statistic value "Dn".

Definition at line 945 of file GoFTest.cxx.

◆ KolmogorovSmirnovTest() [2/2]

void ROOT::Math::GoFTest::KolmogorovSmirnovTest	(	Double_t &	pvalue,
		Double_t &	testStat ) const

Kolmogorov-Smirnov 1-Sample Test.

The Kolmogorov-Smirnov 1-Sample Test algorithm for a specific distribution is described at http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/kstest.htm and described and taken from (4) Press W. H., Teukolsky S.A., Vetterling W.T., Flannery B.P. (2007), Numerical Recipes - The Art of Scientific Computing (Third Edition), Cambridge University Press

Definition at line 921 of file GoFTest.cxx.

◆ LogNormalCDF()

Double_t ROOT::Math::GoFTest::LogNormalCDF ( Double_t x ) const

private

◆ LogSample()

void ROOT::Math::GoFTest::LogSample ( )

private

Applies the logarithm to the sample when the specified distribution to test is LogNormal.

Definition at line 303 of file GoFTest.cxx.

◆ operator()() [1/2]

void ROOT::Math::GoFTest::operator()	(	ETestType	test,
		Double_t &	pvalue,
		Double_t &	testStat ) const

The class's unary functions performing the gif test according to the ETestType provided.

Definition at line 208 of file GoFTest.cxx.

◆ operator()() [2/2]

Double_t ROOT::Math::GoFTest::operator()	(	ETestType	test = kAD,
		const Char_t *	option = "p" ) const

Returns default Anderson Darling 1-Sample Test and default p-value; option "t" returns the test statistic value specific to the test type.

Definition at line 225 of file GoFTest.cxx.

◆ operator=()

GoFTest ROOT::Math::GoFTest::operator= ( GoFTest & gof )

private

Disallowed assign operator.

◆ PValueAD1Sample()

Double_t ROOT::Math::GoFTest::PValueAD1Sample ( Double_t A2 ) const

private

Computation of the 1-Sample Anderson-Darling Test's p-value.

Definition at line 483 of file GoFTest.cxx.

◆ PValueADKSamples()

Double_t ROOT::Math::GoFTest::PValueADKSamples	(	size_t	nsamples,
		Double_t	A2 )

static

Computation of the K-Sample Anderson-Darling Test's p-value as described in (1)

Definition at line 353 of file GoFTest.cxx.

◆ SetCDF()

void ROOT::Math::GoFTest::SetCDF ( )

private

Definition at line 244 of file GoFTest.cxx.

◆ SetDistribution()

void ROOT::Math::GoFTest::SetDistribution	(	EDistribution	dist,
		const std::vector< double > &	distParams = {} )

Sets the distribution for the predefined distribution types and optionally its parameters for 1-sample tests.

Definition at line 124 of file GoFTest.cxx.

◆ SetDistributionFunction()

void ROOT::Math::GoFTest::SetDistributionFunction	(	const IGenFunction &	cdf,
		Bool_t	isPDF,
		Double_t	xmin,
		Double_t	xmax )

private

Definition at line 267 of file GoFTest.cxx.

◆ SetParameters()

void ROOT::Math::GoFTest::SetParameters ( const std::vector< double > & params )

private

Sets the distribution parameters.

Definition at line 204 of file GoFTest.cxx.

◆ SetSamples()

void ROOT::Math::GoFTest::SetSamples	(	std::vector< const Double_t * >	samples,
		const std::vector< size_t >	samplesSizes )

private

set a vector of samples

Definition at line 181 of file GoFTest.cxx.

◆ SetUserCDF() [1/2]

void ROOT::Math::GoFTest::SetUserCDF	(	const IGenFunction &	cdf,
		Double_t	xmin = 1,
		Double_t	xmax = 0 )

inline

Specialization to set the user input distribution as a cumulative distribution function for 1-sample tests.

Definition at line 147 of file GoFTest.h.

◆ SetUserCDF() [2/2]

template<class Dist >

void ROOT::Math::GoFTest::SetUserCDF	(	Dist &	cdf,
		Double_t	xmin = 1,
		Double_t	xmax = 0 )

inline

Sets the user input distribution as a cumulative distribution function for 1-sample tests.

The CDF must return zero for x=xmin and 1 for x=xmax.

Definition at line 142 of file GoFTest.h.

◆ SetUserDistribution() [1/2]

void ROOT::Math::GoFTest::SetUserDistribution	(	const IGenFunction &	dist,
		GoFTest::EUserDistribution	userDist = kPDF,
		Double_t	xmin = 1,
		Double_t	xmax = 0 )

inline

Sets the user input distribution function for 1-sample test using the ROOT::Math::IGenFunction interface.

Definition at line 124 of file GoFTest.h.

◆ SetUserDistribution() [2/2]

template<class Dist >

void ROOT::Math::GoFTest::SetUserDistribution	(	Dist &	dist,
		EUserDistribution	userDist = kPDF,
		Double_t	xmin = 1,
		Double_t	xmax = 0 )

inline

Sets the user input distribution function for 1-sample test as a generic functor object.

Definition at line 118 of file GoFTest.h.

◆ SetUserPDF() [1/2]

void ROOT::Math::GoFTest::SetUserPDF	(	const IGenFunction &	pdf,
		Double_t	xmin = 1,
		Double_t	xmax = 0 )

inline

Specialization to set the user input distribution as a probability density function for 1-sample tests using the ROOT::Math::IGenFunction interface.

Definition at line 135 of file GoFTest.h.

◆ SetUserPDF() [2/2]

template<class Dist >

void ROOT::Math::GoFTest::SetUserPDF	(	Dist &	pdf,
		Double_t	xmin = 1,
		Double_t	xmax = 0 )

inline

Sets the user input distribution as a probability density function for 1-sample tests.

Definition at line 130 of file GoFTest.h.

Member Data Documentation

◆ fCDF

std::unique_ptr<IGenFunction> ROOT::Math::GoFTest::fCDF

private

Pointer to CDF used in 1-sample test.

Definition at line 235 of file GoFTest.h.

◆ fCombinedSamples

std::vector<Double_t> ROOT::Math::GoFTest::fCombinedSamples

private

The combined data.

Definition at line 241 of file GoFTest.h.

◆ fDist

EDistribution ROOT::Math::GoFTest::fDist

private

Type of distribution.

Definition at line 238 of file GoFTest.h.

◆ fParams

std::vector<Double_t> ROOT::Math::GoFTest::fParams

private

The distribution parameters (e.g. fParams[0] = mean, fParams[1] = sigma for a Gaussian)

Definition at line 239 of file GoFTest.h.

◆ fSamples

std::vector<std::vector<Double_t> > ROOT::Math::GoFTest::fSamples

private

The input data.

Definition at line 243 of file GoFTest.h.

◆ fTestSampleFromH0

Bool_t ROOT::Math::GoFTest::fTestSampleFromH0

private

Definition at line 245 of file GoFTest.h.

Libraries for ROOT::Math::GoFTest:

[legend]

The documentation for this class was generated from the following files:

math/mathcore/inc/Math/GoFTest.h
math/mathcore/src/GoFTest.cxx

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Member Enumeration Documentation

◆ EDistribution

◆ ETestType

◆ EUserDistribution

Constructor & Destructor Documentation

◆ GoFTest() [1/6]

◆ GoFTest() [2/6]

◆ GoFTest() [3/6]

◆ GoFTest() [4/6]

◆ ~GoFTest()

◆ GoFTest() [5/6]

◆ GoFTest() [6/6]

Member Function Documentation

◆ AndersonDarling2SamplesTest() [1/3]

◆ AndersonDarling2SamplesTest() [2/3]

◆ AndersonDarling2SamplesTest() [3/3]

◆ AndersonDarlingTest() [1/2]

◆ AndersonDarlingTest() [2/2]

◆ ExponentialCDF()

◆ GaussianCDF()

◆ GetSigmaN()

◆ Instantiate()

◆ InterpolatePValues()

◆ KolmogorovSmirnov2SamplesTest() [1/2]

◆ KolmogorovSmirnov2SamplesTest() [2/2]

◆ KolmogorovSmirnovTest() [1/2]

◆ KolmogorovSmirnovTest() [2/2]

◆ LogNormalCDF()

◆ LogSample()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator=()

◆ PValueAD1Sample()

◆ PValueADKSamples()

◆ SetCDF()

◆ SetDistribution()

◆ SetDistributionFunction()

◆ SetParameters()

◆ SetSamples()

◆ SetUserCDF() [1/2]

◆ SetUserCDF() [2/2]

◆ SetUserDistribution() [1/2]

◆ SetUserDistribution() [2/2]

◆ SetUserPDF() [1/2]

◆ SetUserPDF() [2/2]

Member Data Documentation

◆ fCDF

◆ fCombinedSamples

◆ fDist

◆ fParams

◆ fSamples

◆ fTestSampleFromH0