itk::Statistics::ProbabilityDistribution Class Reference

#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
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
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
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)
void	SetDebug (bool debugFlag) const
void	SetReferenceCount (int) override
void	UnRegister () const noexceptoverride
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
virtual void	Delete ()
virtual int	GetReferenceCount () const
	itkCloneMacro (Self)
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 &time)
	~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 flag)
Static Public Member Functions inherited from itk::LightObject
static void	BreakOnError ()
static Pointer	New ()

Member Typedef Documentation

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

Definition at line 82 of file itkProbabilityDistribution.h.

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

Type of the parameter vector.

Definition at line 88 of file itkProbabilityDistribution.h.

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

Definition at line 81 of file itkProbabilityDistribution.h.

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

Standard class type aliases

Definition at line 79 of file itkProbabilityDistribution.h.

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

Definition at line 80 of file itkProbabilityDistribution.h.

Constructor & Destructor Documentation

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

protected

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

overrideprotected

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::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.

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

ParametersType itk::Statistics::ProbabilityDistribution::m_Parameters

protected

Definition at line 155 of file itkProbabilityDistribution.h.

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

• itkProbabilityDistribution.h