ITK  5.2.0
Insight Toolkit
Public Types | Public Member Functions | Static Public Member Functions | Protected Member Functions | List of all members
itk::Statistics::TDistribution Class Reference

#include <itkTDistribution.h>

+ Inheritance diagram for itk::Statistics::TDistribution:
+ Collaboration diagram for itk::Statistics::TDistribution:

Public Types

using ConstPointer = SmartPointer< const Self >
 
using Pointer = SmartPointer< Self >
 
using Self = TDistribution
 
using Superclass = ProbabilityDistribution
 
- Public Types inherited from itk::Statistics::ProbabilityDistribution
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 ::itk::LightObject::Pointer CreateAnother () const
 
double EvaluateCDF (double x) const override
 
double EvaluateCDF (double x, const ParametersType &) const override
 
virtual double EvaluateCDF (double x, SizeValueType degreesOfFreedom) const
 
double EvaluateInverseCDF (double p) const override
 
double EvaluateInverseCDF (double p, const ParametersType &) const override
 
virtual double EvaluateInverseCDF (double p, SizeValueType degreesOfFreedom) const
 
double EvaluatePDF (double x) const override
 
double EvaluatePDF (double x, const ParametersType &) const override
 
virtual double EvaluatePDF (double x, SizeValueType degreesOfFreedom) const
 
virtual SizeValueType GetDegreesOfFreedom () const
 
double GetMean () const override
 
virtual const char * GetNameOfClass () const
 
SizeValueType GetNumberOfParameters () const override
 
double GetVariance () const override
 
bool HasMean () const override
 
bool HasVariance () const override
 
virtual void SetDegreesOfFreedom (SizeValueType)
 
- Public Member Functions inherited from itk::Statistics::ProbabilityDistribution
virtual const ParametersTypeGetParameters () const
 
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 void DebugOff () const
 
virtual void DebugOn () const
 
CommandGetCommand (unsigned long tag)
 
bool GetDebug () const
 
MetaDataDictionaryGetMetaDataDictionary ()
 
const MetaDataDictionaryGetMetaDataDictionary () const
 
virtual ModifiedTimeType GetMTime () const
 
virtual const TimeStampGetTimeStamp () 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 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
virtual void Delete ()
 
virtual int GetReferenceCount () const
 
 itkCloneMacro (Self)
 
void Print (std::ostream &os, Indent indent=0) const
 

Static Public Member Functions

static double CDF (double x, const ParametersType &)
 
static double CDF (double x, SizeValueType degreesOfFreedom)
 
static double InverseCDF (double p, const ParametersType &)
 
static double InverseCDF (double p, SizeValueType degreesOfFreedom)
 
static Pointer New ()
 
static double PDF (double x, const ParametersType &)
 
static double PDF (double x, SizeValueType degreesOfFreedom)
 
- 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 ()
 

Protected Member Functions

void PrintSelf (std::ostream &os, Indent indent) const override
 
 TDistribution ()
 
 ~TDistribution () override=default
 
- Protected Member Functions inherited from itk::Statistics::ProbabilityDistribution
 ProbabilityDistribution ()
 
 ~ProbabilityDistribution () override
 
- Protected Member Functions inherited from itk::Object
 Object ()
 
 ~Object () override
 
bool PrintObservers (std::ostream &os, Indent indent) const
 
virtual void SetTimeStamp (const TimeStamp &time)
 
- 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 ()
 

Additional Inherited Members

- Protected Attributes inherited from itk::Statistics::ProbabilityDistribution
ParametersType m_Parameters
 
- Protected Attributes inherited from itk::LightObject
std::atomic< int > m_ReferenceCount
 

Detailed Description

TDistribution class defines the interface for a univariate Student-t distribution (pdfs, cdfs, etc.).

TDistribution provides access to the probability density function (pdf), the cumulative distribution function (cdf), and the inverse cumulative distribution function for a Student-t 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 provided. The static methods allow for optimized access to distributions when the distribution is known a priori to the algorithm.

TDistributions 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).

TDistributions can be used for t tests.

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 59 of file itkTDistribution.h.

Member Typedef Documentation

◆ ConstPointer

Definition at line 68 of file itkTDistribution.h.

◆ Pointer

Definition at line 67 of file itkTDistribution.h.

◆ Self

Standard class type aliases

Definition at line 65 of file itkTDistribution.h.

◆ Superclass

Definition at line 66 of file itkTDistribution.h.

Constructor & Destructor Documentation

◆ TDistribution()

itk::Statistics::TDistribution::TDistribution ( )
protected

◆ ~TDistribution()

itk::Statistics::TDistribution::~TDistribution ( )
overrideprotecteddefault

Member Function Documentation

◆ CDF() [1/2]

static double itk::Statistics::TDistribution::CDF ( double  x,
const ParametersType  
)
static

Static method to evaluate the cumulative distribution function (cdf) of a Student-t with a specified number of degrees of freedom. The static method provides optimized access without requiring an instance of the class. The degrees of freedom are passed as a parameters vector.

This is based on Abramowitz and Stegun 26.7.1. Accuracy is approximately 10^-14.

◆ CDF() [2/2]

static double itk::Statistics::TDistribution::CDF ( double  x,
SizeValueType  degreesOfFreedom 
)
static

Static method to evaluate the cumulative distribution function (cdf) of a Student-t with a specified number of degrees of freedom. The static method provides optimized access without requiring an instance of the class.

This is based on Abramowitz and Stegun 26.7.1. Accuracy is approximately 10^-14.

◆ CreateAnother()

virtual::itk::LightObject::Pointer itk::Statistics::TDistribution::CreateAnother ( ) const
virtual

Create an object from an instance, potentially deferring to a factory. This method allows you to create an instance of an object that is exactly the same type as the referring object. This is useful in cases where an object has been cast back to a base class.

Reimplemented from itk::Object.

◆ EvaluateCDF() [1/3]

double itk::Statistics::TDistribution::EvaluateCDF ( double  x) const
overridevirtual

Evaluate the cumulative distribution function (cdf). The parameters of the distribution are assigned via SetParameters().

Implements itk::Statistics::ProbabilityDistribution.

◆ EvaluateCDF() [2/3]

double itk::Statistics::TDistribution::EvaluateCDF ( double  x,
const ParametersType  
) const
overridevirtual

Evaluate the cumulative distribution function (cdf). The parameters for the distribution are passed as a parameters vector. The ordering of the parameters is (degreesOfFreedom).

Implements itk::Statistics::ProbabilityDistribution.

◆ EvaluateCDF() [3/3]

virtual double itk::Statistics::TDistribution::EvaluateCDF ( double  x,
SizeValueType  degreesOfFreedom 
) const
virtual

Evaluate the cumulative distribution function (cdf). The parameters of the distribution are passed as separate parameters.

◆ EvaluateInverseCDF() [1/3]

double itk::Statistics::TDistribution::EvaluateInverseCDF ( double  p) const
overridevirtual

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().

Implements itk::Statistics::ProbabilityDistribution.

◆ EvaluateInverseCDF() [2/3]

double itk::Statistics::TDistribution::EvaluateInverseCDF ( double  p,
const ParametersType  
) const
overridevirtual

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. The ordering of the parameters is (degrees of freedom).

Implements itk::Statistics::ProbabilityDistribution.

◆ EvaluateInverseCDF() [3/3]

virtual double itk::Statistics::TDistribution::EvaluateInverseCDF ( double  p,
SizeValueType  degreesOfFreedom 
) const
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 passed as separate parameters.

◆ EvaluatePDF() [1/3]

double itk::Statistics::TDistribution::EvaluatePDF ( double  x) const
overridevirtual

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

Implements itk::Statistics::ProbabilityDistribution.

◆ EvaluatePDF() [2/3]

double itk::Statistics::TDistribution::EvaluatePDF ( double  x,
const ParametersType  
) const
overridevirtual

Evaluate the probability density function (pdf). The parameters for the distribution are passed as a parameters vector. The ordering of the parameters is (degrees of freedom).

Implements itk::Statistics::ProbabilityDistribution.

◆ EvaluatePDF() [3/3]

virtual double itk::Statistics::TDistribution::EvaluatePDF ( double  x,
SizeValueType  degreesOfFreedom 
) const
virtual

Evaluate the probability density function (pdf). The parameters of the distribution are passed as separate parameters.

◆ GetDegreesOfFreedom()

virtual SizeValueType itk::Statistics::TDistribution::GetDegreesOfFreedom ( ) const
virtual

Get the number of degrees of freedom in the t distribution. Defaults to 1

◆ GetMean()

double itk::Statistics::TDistribution::GetMean ( ) const
overridevirtual

Get the mean of the distribution.

Implements itk::Statistics::ProbabilityDistribution.

◆ GetNameOfClass()

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

Strandard macros

Reimplemented from itk::Statistics::ProbabilityDistribution.

◆ GetNumberOfParameters()

SizeValueType itk::Statistics::TDistribution::GetNumberOfParameters ( ) const
inlineoverridevirtual

Return the number of parameters. For a univariate Student-t distribution, the number of parameters is 1 (degrees of freedom)

Implements itk::Statistics::ProbabilityDistribution.

Definition at line 79 of file itkTDistribution.h.

◆ GetVariance()

double itk::Statistics::TDistribution::GetVariance ( ) const
overridevirtual

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

Implements itk::Statistics::ProbabilityDistribution.

◆ HasMean()

bool itk::Statistics::TDistribution::HasMean ( ) const
inlineoverridevirtual

Does the Student-t distribution have a mean?

Implements itk::Statistics::ProbabilityDistribution.

Definition at line 146 of file itkTDistribution.h.

◆ HasVariance()

bool itk::Statistics::TDistribution::HasVariance ( ) const
overridevirtual

Does the Student-t distribution have a variance? Variance is only defined for degrees of freedom greater than 2

Implements itk::Statistics::ProbabilityDistribution.

◆ InverseCDF() [1/2]

static double itk::Statistics::TDistribution::InverseCDF ( double  p,
const ParametersType  
)
static

Static method to evaluate the inverse cumulative distribution function of a Student-t with a specified number of degrees of freedom. The static method provides optimized access without requiring an instance of the class. Parameter p must be between 0.0 and 1.0. The degrees of freedom are passed as a parameters vector.

This is based on Abramowitz and Stegun 26.7.5 followed by a few Newton iterations to improve the precision at low degrees of freedom. Accuracy is approximately 10^-10.

◆ InverseCDF() [2/2]

static double itk::Statistics::TDistribution::InverseCDF ( double  p,
SizeValueType  degreesOfFreedom 
)
static

Static method to evaluate the inverse cumulative distribution function of a Student-t with a specified number of degrees of freedom. The static method provides optimized access without requiring an instance of the class. Parameter p must be between 0.0 and 1.0.

This is based on Abramowitz and Stegun 26.7.5 followed by a few Newton iterations to improve the precision at low degrees of freedom. Accuracy is approximately 10^-10.

◆ New()

static Pointer itk::Statistics::TDistribution::New ( )
static

Method for creation through the object factory.

◆ PDF() [1/2]

static double itk::Statistics::TDistribution::PDF ( double  x,
const ParametersType  
)
static

Static method to evaluate the probability density function (pdf) of a Student-t with a specified number of degrees of freedom. The static method provides optimized access without requiring an instance of the class. The degrees of freedom for the distribution are passed in a parameters vector.

◆ PDF() [2/2]

static double itk::Statistics::TDistribution::PDF ( double  x,
SizeValueType  degreesOfFreedom 
)
static

Static method to evaluate the probability density function (pdf) of a Student-t with a specified number of degrees of freedom. The static method provides optimized access without requiring an instance of the class.

◆ PrintSelf()

void itk::Statistics::TDistribution::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::Statistics::ProbabilityDistribution.

◆ SetDegreesOfFreedom()

virtual void itk::Statistics::TDistribution::SetDegreesOfFreedom ( SizeValueType  )
virtual

Set the number of degrees of freedom in the Student-t distribution. Defaults to 1


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