#include <itkProbabilityDistribution.h>

Detailed Description

ProbabilityDistribution class defines common interface for statistical distributions (pdfs, cdfs, etc.).

ProbabilityDistribution defines a common interface for parametric and non-parametric distributions. ProbabilityDistribution provides access to the probability density function (pdf), the cumulative distribution function (cdf), and the inverse cumulative distribution function.

ProbabilityDistribution also defines an abstract interface for setting parameters of distribution (mean/variance for a Gaussian, degrees of freedom for Student-t, etc.).

Note that nonparametric subclasses of ProbabilityDistribution are possible. For instance, a nonparametric implementation may use a histogram or kernel density function to model the distribution.

The EvaluatePDF(), EvaluateCDF, EvaluateInverseCDF() methods are all virtual, allowing algorithms to be written with an abstract interface to a distribution (with said distribution provided to the algorithm at run-time). Static methods, not requiring an instance of the distribution, are also allowed. The static methods allow for optimized access to distributions when the distribution is known a priori to the algorithm.

ProbabilityDistributions are univariate. Multivariate versions may be provided under a separate superclass (since the parameters to the pdf and cdf would have to be vectors not scalars). Perhaps this class will be named MultivariateProbabilityDistribution.

ProbabilityDistributions can be used for standard statistical tests: Z-scores, t-tests, chi-squared tests, F-tests, etc.

Note: This work is part of the National Alliance for Medical Image Computing (NAMIC), funded by the National Institutes of Health through the NIH Roadmap for Medical Research, Grant U54 EB005149. Information on the National Centers for Biomedical Computing can be obtained from http://commonfund.nih.gov/bioinformatics.

Definition at line 72 of file itkProbabilityDistribution.h.

Inheritance diagram for itk::Statistics::ProbabilityDistribution:

Collaboration diagram for itk::Statistics::ProbabilityDistribution:

Public Types
using	ConstPointer = SmartPointer< const Self >

using	ParametersType = Array< double >

using	Pointer = SmartPointer< Self >

using	Self = ProbabilityDistribution

using	Superclass = Object

Public Types inherited from itk::Object
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	Self = Object

using	Superclass = LightObject

Public Types inherited from itk::LightObject
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	Self = LightObject

Public Member Functions
virtual double	EvaluateCDF (double x) const =0

virtual double	EvaluateCDF (double x, const ParametersType &) const =0

virtual double	EvaluateInverseCDF (double p) const =0

virtual double	EvaluateInverseCDF (double p, const ParametersType &) const =0

virtual double	EvaluatePDF (double x) const =0

virtual double	EvaluatePDF (double x, const ParametersType &) const =0

virtual double	GetMean () const =0

const char *	GetNameOfClass () const override

virtual SizeValueType	GetNumberOfParameters () const =0

virtual const ParametersType &	GetParameters () const

virtual double	GetVariance () const =0

virtual bool	HasMean () const =0

virtual bool	HasVariance () const =0

virtual void	SetParameters (const ParametersType &params)

Public Member Functions inherited from itk::Object
unsigned long	AddObserver (const EventObject &event, Command *cmd) const

unsigned long	AddObserver (const EventObject &event, std::function< void(const EventObject &)> function) const

LightObject::Pointer	CreateAnother () const override

virtual void	DebugOff () const

virtual void	DebugOn () const

Command *	GetCommand (unsigned long tag)

bool	GetDebug () const

MetaDataDictionary &	GetMetaDataDictionary ()

const MetaDataDictionary &	GetMetaDataDictionary () const

virtual ModifiedTimeType	GetMTime () const

virtual const TimeStamp &	GetTimeStamp () const

bool	HasObserver (const EventObject &event) const

void	InvokeEvent (const EventObject &)

void	InvokeEvent (const EventObject &) const

virtual void	Modified () const

void	Register () const override

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag) const

void	SetDebug (bool debugFlag) const

void	SetReferenceCount (int) override

void	UnRegister () const noexcept override

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

void	SetMetaDataDictionary (MetaDataDictionary &&rrhs)

virtual void	SetObjectName (std::string _arg)

virtual const std::string &	GetObjectName () const

Public Member Functions inherited from itk::LightObject
Pointer	Clone () const

virtual void	Delete ()

virtual int	GetReferenceCount () const

void	Print (std::ostream &os, Indent indent=0) const

Protected Member Functions
void	PrintSelf (std::ostream &os, Indent indent) const override

	ProbabilityDistribution ()

	~ProbabilityDistribution () override

Protected Member Functions inherited from itk::Object
	Object ()

bool	PrintObservers (std::ostream &os, Indent indent) const

virtual void	SetTimeStamp (const TimeStamp &timeStamp)

	~Object () override

Protected Member Functions inherited from itk::LightObject
virtual LightObject::Pointer	InternalClone () const

	LightObject ()

virtual void	PrintHeader (std::ostream &os, Indent indent) const

virtual void	PrintTrailer (std::ostream &os, Indent indent) const

virtual	~LightObject ()

Protected Attributes
ParametersType	m_Parameters {}

Protected Attributes inherited from itk::LightObject
std::atomic< int >	m_ReferenceCount {}

Additional Inherited Members
Static Public Member Functions inherited from itk::Object
static bool	GetGlobalWarningDisplay ()

static void	GlobalWarningDisplayOff ()

static void	GlobalWarningDisplayOn ()

static Pointer	New ()

static void	SetGlobalWarningDisplay (bool val)

Static Public Member Functions inherited from itk::LightObject
static void	BreakOnError ()

static Pointer	New ()

Member Typedef Documentation

◆ ConstPointer

using itk::Statistics::ProbabilityDistribution::ConstPointer = SmartPointer<const Self>

Definition at line 81 of file itkProbabilityDistribution.h.

◆ ParametersType

using itk::Statistics::ProbabilityDistribution::ParametersType = Array<double>

Type of the parameter vector.

Definition at line 87 of file itkProbabilityDistribution.h.

◆ Pointer

using itk::Statistics::ProbabilityDistribution::Pointer = SmartPointer<Self>

Definition at line 80 of file itkProbabilityDistribution.h.

◆ Self

using itk::Statistics::ProbabilityDistribution::Self = ProbabilityDistribution

Standard class type aliases

Definition at line 78 of file itkProbabilityDistribution.h.

◆ Superclass

using itk::Statistics::ProbabilityDistribution::Superclass = Object

Definition at line 79 of file itkProbabilityDistribution.h.

Constructor & Destructor Documentation

◆ ProbabilityDistribution()

itk::Statistics::ProbabilityDistribution::ProbabilityDistribution ( )

protected

◆ ~ProbabilityDistribution()

itk::Statistics::ProbabilityDistribution::~ProbabilityDistribution ( )

overrideprotected

Member Function Documentation

◆ EvaluateCDF() [1/2]

virtual double itk::Statistics::ProbabilityDistribution::EvaluateCDF ( double x ) const

pure virtual

Evaluate the cumulative distribution function (cdf). The parameters of the distribution are assigned via SetParameters(). See concrete subclasses for the ordering of parameters.

Implemented in itk::Statistics::GaussianDistribution, itk::Statistics::TDistribution, and itk::Statistics::ChiSquareDistribution.

◆ EvaluateCDF() [2/2]

virtual double itk::Statistics::ProbabilityDistribution::EvaluateCDF	(	double	x,
		const ParametersType &
	)		const

pure virtual

Evaluate the cumulative distribution function (cdf). The parameters for the distribution are passed as a parameters vector. See concrete subclasses for the ordering of parameters.

Implemented in itk::Statistics::GaussianDistribution, itk::Statistics::TDistribution, and itk::Statistics::ChiSquareDistribution.

◆ EvaluateInverseCDF() [1/2]

virtual double itk::Statistics::ProbabilityDistribution::EvaluateInverseCDF ( double p ) const

pure virtual

Evaluate the inverse cumulative distribution function (inverse cdf). Parameter p must be between 0.0 and 1.0. The parameters of the distribution are assigned via SetParameters(). See concrete subclasses for the ordering of parameters.

Implemented in itk::Statistics::GaussianDistribution, itk::Statistics::TDistribution, and itk::Statistics::ChiSquareDistribution.

◆ EvaluateInverseCDF() [2/2]

virtual double itk::Statistics::ProbabilityDistribution::EvaluateInverseCDF	(	double	p,
		const ParametersType &
	)		const

pure virtual

Evaluate the inverse cumulative distribution function (inverse cdf). Parameter p must be between 0.0 and 1.0. The parameters for the distribution are passed as a parameters vector. See concrete subclasses for the ordering of parameters.

Implemented in itk::Statistics::GaussianDistribution, itk::Statistics::TDistribution, and itk::Statistics::ChiSquareDistribution.

◆ EvaluatePDF() [1/2]

virtual double itk::Statistics::ProbabilityDistribution::EvaluatePDF ( double x ) const

pure virtual

Evaluate the probability density function (pdf). The parameters of the distribution are assigned via SetParameters().

Implemented in itk::Statistics::GaussianDistribution, itk::Statistics::TDistribution, and itk::Statistics::ChiSquareDistribution.

◆ EvaluatePDF() [2/2]

virtual double itk::Statistics::ProbabilityDistribution::EvaluatePDF	(	double	x,
		const ParametersType &
	)		const

pure virtual

Evaluate the probability density function (pdf). The parameters for the distribution are passed as a parameters vector. See concrete subclasses for the ordering of parameters.

Implemented in itk::Statistics::GaussianDistribution, itk::Statistics::TDistribution, and itk::Statistics::ChiSquareDistribution.

◆ GetMean()

virtual double itk::Statistics::ProbabilityDistribution::GetMean ( ) const

pure virtual

Get the mean of the distribution. If the mean does not exist, then quiet_NaN may is returned.

Implemented in itk::Statistics::TDistribution, itk::Statistics::ChiSquareDistribution, and itk::Statistics::GaussianDistribution.

◆ GetNameOfClass()

const char* itk::Statistics::ProbabilityDistribution::GetNameOfClass ( ) const

overridevirtual

See also: LightObject::GetNameOfClass()

Reimplemented from itk::Object.

Reimplemented in itk::Statistics::TDistribution.

◆ GetNumberOfParameters()

virtual SizeValueType itk::Statistics::ProbabilityDistribution::GetNumberOfParameters ( ) const

pure virtual

Return the number of parameters that describe the distribution. For nonparametric distributions, this will be a function of the number of samples.

Implemented in itk::Statistics::GaussianDistribution, itk::Statistics::TDistribution, and itk::Statistics::ChiSquareDistribution.

◆ GetParameters()

virtual const ParametersType& itk::Statistics::ProbabilityDistribution::GetParameters ( ) const

virtual

Get the parameters of the distribution. See concrete subclasses for the order of parameters. Subclasses may provide convenience methods for setting parameters, i.e. SetDegreesOfFreedom(), etc.

◆ GetVariance()

virtual double itk::Statistics::ProbabilityDistribution::GetVariance ( ) const

pure virtual

Get the variance of the distribution. If the variance does not exist, then quiet_NaN is returned.

Implemented in itk::Statistics::ChiSquareDistribution, itk::Statistics::GaussianDistribution, and itk::Statistics::TDistribution.

◆ HasMean()

virtual bool itk::Statistics::ProbabilityDistribution::HasMean ( ) const

pure virtual

Does this distribution have a mean?

Implemented in itk::Statistics::GaussianDistribution, itk::Statistics::TDistribution, and itk::Statistics::ChiSquareDistribution.

◆ HasVariance()

virtual bool itk::Statistics::ProbabilityDistribution::HasVariance ( ) const

pure virtual

Does this distribution have a variance?

Implemented in itk::Statistics::GaussianDistribution, itk::Statistics::TDistribution, and itk::Statistics::ChiSquareDistribution.

◆ PrintSelf()

void itk::Statistics::ProbabilityDistribution::PrintSelf	(	std::ostream &	os,
		Indent	indent
	)		const

overrideprotectedvirtual

Methods invoked by Print() to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from itk::Object.

Reimplemented in itk::Statistics::TDistribution.

◆ SetParameters()

virtual void itk::Statistics::ProbabilityDistribution::SetParameters ( const ParametersType & params )

virtual

Set the parameters of the distribution. See concrete subclasses for the order of the parameters. Subclasses may provide convenience methods for setting parameters, i.e. SetDegreesOfFreedom(), etc.

Member Data Documentation

◆ m_Parameters

ParametersType itk::Statistics::ProbabilityDistribution::m_Parameters {}

protected

Definition at line 167 of file itkProbabilityDistribution.h.

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

itkProbabilityDistribution.h

Detailed Description

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Member Typedef Documentation

◆ ConstPointer

◆ ParametersType

◆ Pointer

◆ Self

◆ Superclass

Constructor & Destructor Documentation

◆ ProbabilityDistribution()

◆ ~ProbabilityDistribution()

Member Function Documentation

◆ EvaluateCDF() [1/2]

◆ EvaluateCDF() [2/2]

◆ EvaluateInverseCDF() [1/2]

◆ EvaluateInverseCDF() [2/2]

◆ EvaluatePDF() [1/2]

◆ EvaluatePDF() [2/2]

◆ GetMean()

◆ GetNameOfClass()

◆ GetNumberOfParameters()

◆ GetParameters()

◆ GetVariance()

◆ HasMean()

◆ HasVariance()

◆ PrintSelf()

◆ SetParameters()

Member Data Documentation

◆ m_Parameters