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itk::Statistics::TDistribution Class Reference

#include <itkTDistribution.h>

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

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 58 of file itkTDistribution.h.

Public Types

typedef SmartPointer< const SelfConstPointer
 
typedef SmartPointer< SelfPointer
 
typedef TDistribution Self
 
typedef ProbabilityDistribution Superclass
 
- Public Types inherited from itk::Statistics::ProbabilityDistribution
typedef SmartPointer< const SelfConstPointer
 
typedef Array< double > ParametersType
 
typedef SmartPointer< SelfPointer
 
typedef ProbabilityDistribution Self
 
typedef Object Superclass
 
- Public Types inherited from itk::Object
typedef SmartPointer< const SelfConstPointer
 
typedef SmartPointer< SelfPointer
 
typedef Object Self
 
typedef LightObject Superclass
 
- Public Types inherited from itk::LightObject
typedef SmartPointer< const SelfConstPointer
 
typedef SmartPointer< SelfPointer
 
typedef LightObject Self
 

Public Member Functions

virtual ::itk::LightObject::Pointer CreateAnother () const
 
virtual double EvaluateCDF (double x) const override
 
virtual double EvaluateCDF (double x, const ParametersType &) const override
 
virtual double EvaluateCDF (double x, SizeValueType degreesOfFreedom) const
 
virtual double EvaluateInverseCDF (double p) const override
 
virtual double EvaluateInverseCDF (double p, const ParametersType &) const override
 
virtual double EvaluateInverseCDF (double p, SizeValueType degreesOfFreedom) const
 
virtual double EvaluatePDF (double x) const override
 
virtual double EvaluatePDF (double x, const ParametersType &) const override
 
virtual double EvaluatePDF (double x, SizeValueType degreesOfFreedom) const
 
virtual SizeValueType GetDegreesOfFreedom () const
 
virtual double GetMean () const override
 
virtual const char * GetNameOfClass () const
 
virtual SizeValueType GetNumberOfParameters () const override
 
virtual double GetVariance () const override
 
virtual bool HasMean () const override
 
virtual 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
 
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
 

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

virtual void PrintSelf (std::ostream &os, Indent indent) const override
 
 TDistribution ()
 
virtual ~TDistribution (void)
 
- Protected Member Functions inherited from itk::Statistics::ProbabilityDistribution
 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 ()
 

Private Member Functions

void operator= (const Self &) ITK_DELETE_FUNCTION
 
 TDistribution (const Self &) ITK_DELETE_FUNCTION
 

Additional Inherited Members

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

Member Typedef Documentation

Definition at line 66 of file itkTDistribution.h.

Definition at line 65 of file itkTDistribution.h.

Standard class typedefs

Definition at line 63 of file itkTDistribution.h.

Definition at line 64 of file itkTDistribution.h.

Constructor & Destructor Documentation

itk::Statistics::TDistribution::TDistribution ( )
protected
virtual itk::Statistics::TDistribution::~TDistribution ( void  )
inlineprotectedvirtual

Definition at line 202 of file itkTDistribution.h.

itk::Statistics::TDistribution::TDistribution ( const Self )
private

Member Function Documentation

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.

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.

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.

virtual 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.

virtual 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.

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.

virtual 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.

virtual 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.

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.

virtual 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.

virtual 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.

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.

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

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

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

Get the mean of the distribution.

Implements itk::Statistics::ProbabilityDistribution.

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

Strandard macros

Reimplemented from itk::Statistics::ProbabilityDistribution.

virtual 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 76 of file itkTDistribution.h.

virtual 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.

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

Does the Student-t distribution have a mean?

Implements itk::Statistics::ProbabilityDistribution.

Definition at line 129 of file itkTDistribution.h.

virtual 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.

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.

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.

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

Method for creation through the object factory.

void itk::Statistics::TDistribution::operator= ( const Self )
private
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.

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.

virtual 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.

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: