#include <itkTDistribution.h>

Inheritance diagram for itk::Statistics::TDistribution:

Collaboration diagram for itk::Statistics::TDistribution:

Public Types
typedef SmartPointer< const Self >	ConstPointer
typedef SmartPointer< Self >	Pointer
typedef TDistribution	Self
typedef ProbabilityDistribution	Superclass
Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother (void) const
virtual double	EvaluateCDF (double x) const
virtual double	EvaluateCDF (double x, const ParametersType &) const
virtual double	EvaluateCDF (double x, SizeValueType degreesOfFreedom) const
virtual double	EvaluateInverseCDF (double p) const
virtual double	EvaluateInverseCDF (double p, const ParametersType &) const
virtual double	EvaluateInverseCDF (double p, SizeValueType degreesOfFreedom) const
virtual double	EvaluatePDF (double x) const
virtual double	EvaluatePDF (double x, const ParametersType &) const
virtual double	EvaluatePDF (double x, SizeValueType degreesOfFreedom) const
virtual SizeValueType	GetDegreesOfFreedom () const
virtual double	GetMean () const
virtual const char *	GetNameOfClass () const
virtual SizeValueType	GetNumberOfParameters () const
virtual double	GetVariance () const
virtual bool	HasMean () const
virtual bool	HasVariance () const
virtual void	SetDegreesOfFreedom (SizeValueType)
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)
Protected Member Functions
void	PrintSelf (std::ostream &os, Indent indent) const
	TDistribution (void)
virtual	~TDistribution (void)
Private Member Functions
void	operator= (const Self &)
	TDistribution (const Self &)

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 57 of file itkTDistribution.h.

Member Typedef Documentation

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

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 65 of file itkTDistribution.h.

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

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 64 of file itkTDistribution.h.

typedef TDistribution itk::Statistics::TDistribution::Self

Standard class typedefs

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 62 of file itkTDistribution.h.

typedef ProbabilityDistribution itk::Statistics::TDistribution::Superclass

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 63 of file itkTDistribution.h.

Constructor & Destructor Documentation

itk::Statistics::TDistribution::TDistribution ( void ) [protected]

virtual itk::Statistics::TDistribution::~TDistribution ( void ) [inline, protected, virtual]

Definition at line 201 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 ( void ) 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 [virtual]

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 `[virtual]`

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 [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().

Implements itk::Statistics::ProbabilityDistribution.

virtual double itk::Statistics::TDistribution::EvaluateInverseCDF	(	double	p,
		const ParametersType &
	)		const `[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. 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 [virtual]

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 `[virtual]`

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 [virtual]

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 [inline, virtual]

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 75 of file itkTDistribution.h.

virtual double itk::Statistics::TDistribution::GetVariance ( ) const [virtual]

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 [inline, virtual]

Does the Student-t distribution have a mean?

Implements itk::Statistics::ProbabilityDistribution.

Definition at line 128 of file itkTDistribution.h.

virtual bool itk::Statistics::TDistribution::HasVariance ( ) const [virtual]

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.

Reimplemented from itk::Object.

void itk::Statistics::TDistribution::operator= ( const Self & ) [private]

Mutex lock to protect modification to the reference count

Reimplemented from itk::Statistics::ProbabilityDistribution.

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.

void itk::Statistics::TDistribution::PrintSelf	(	std::ostream &	os,
		Indent	indent
	)		const `[protected, virtual]`

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:

itkTDistribution.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Private Member Functions

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation