#include <itkProbabilityDistribution.h>

Inheritance diagram for itk::Statistics::ProbabilityDistribution:

Collaboration diagram for itk::Statistics::ProbabilityDistribution:

Detailed Description

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

ProbabilityDistribution defines a common interface for parameteric 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.

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef Array< double >	ParametersType

typedef SmartPointer< Self >	Pointer

typedef ProbabilityDistribution	Self

typedef Object	Superclass

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

typedef SmartPointer< Self >	Pointer

typedef Object	Self

typedef LightObject	Superclass

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

typedef SmartPointer< Self >	Pointer

typedef LightObject	Self

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

virtual const char *	GetNameOfClass () const

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 *)

unsigned long	AddObserver (const EventObject &event, Command *) const

virtual 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

virtual void	Register () const override

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag)

void	SetDebug (bool debugFlag) const

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

virtual void	SetReferenceCount (int) override

virtual void	UnRegister () const noexceptoverride

virtual void	SetObjectName (std::string _arg)

virtual const std::string &	GetObjectName () const

Public Member Functions inherited from itk::LightObject
virtual void	Delete ()

virtual int	GetReferenceCount () const

	itkCloneMacro (Self)

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

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

	ProbabilityDistribution (void)

virtual	~ProbabilityDistribution (void)

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

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

virtual void	SetTimeStamp (const TimeStamp &time)

virtual	~Object ()

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
AtomicInt< int >	m_ReferenceCount

Private Member Functions
void	operator= (const Self &)

	ProbabilityDistribution (const Self &)

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 flag)

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

static Pointer	New ()

Member Typedef Documentation

typedef SmartPointer< const Self > itk::Statistics::ProbabilityDistribution::ConstPointer

Definition at line 80 of file itkProbabilityDistribution.h.

typedef Array< double > itk::Statistics::ProbabilityDistribution::ParametersType

Type of the parameter vector.

Definition at line 83 of file itkProbabilityDistribution.h.

typedef SmartPointer< Self > itk::Statistics::ProbabilityDistribution::Pointer

Definition at line 79 of file itkProbabilityDistribution.h.

typedef ProbabilityDistribution itk::Statistics::ProbabilityDistribution::Self

Standard class typedefs

Definition at line 77 of file itkProbabilityDistribution.h.

typedef Object itk::Statistics::ProbabilityDistribution::Superclass

Definition at line 78 of file itkProbabilityDistribution.h.

Constructor & Destructor Documentation

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

protected

virtual itk::Statistics::ProbabilityDistribution::~ProbabilityDistribution ( void )

protectedvirtual

itk::Statistics::ProbabilityDistribution::ProbabilityDistribution ( const Self & )

private

Member Function Documentation

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::ChiSquareDistribution, and itk::Statistics::TDistribution.

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::ChiSquareDistribution, and itk::Statistics::TDistribution.

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::ChiSquareDistribution, and itk::Statistics::TDistribution.

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::ChiSquareDistribution, and itk::Statistics::TDistribution.

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::ChiSquareDistribution, and itk::Statistics::TDistribution.

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::ChiSquareDistribution, and itk::Statistics::TDistribution.

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

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

virtual

Standard macros

Reimplemented from itk::Object.

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

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::ChiSquareDistribution, and itk::Statistics::TDistribution.

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.

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

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

pure virtual

Does this distribution have a mean?

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

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.

void itk::Statistics::ProbabilityDistribution::operator= ( const Self & )

private

virtual 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::GaussianDistribution, itk::Statistics::TDistribution, and itk::Statistics::ChiSquareDistribution.

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.