ITK  4.2.0
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Public Types | Public Member Functions | Static Public Member Functions | Protected Member Functions | Private Member Functions
itk::Statistics::GaussianDistribution Class Reference
Module ITKStatistics

#include <itkGaussianDistribution.h>

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

List of all members.

Public Types

typedef SmartPointer< const Self > ConstPointer
typedef SmartPointer< Self > Pointer
typedef GaussianDistribution Self
typedef ProbabilityDistribution Superclass
- Public Types inherited from itk::Statistics::ProbabilityDistribution
typedef Array< double > ParametersType
- Public Types inherited from itk::Object
- Public Types inherited from itk::LightObject

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, double mean, double variance) const
virtual double EvaluateInverseCDF (double p) const
virtual double EvaluateInverseCDF (double p, const ParametersType &) const
virtual double EvaluateInverseCDF (double p, double mean, double variance) const
virtual double EvaluatePDF (double x) const
virtual double EvaluatePDF (double x, const ParametersType &) const
virtual double EvaluatePDF (double x, double mean, double variance) 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 SetMean (double)
virtual void SetVariance (double)
- Public Member Functions inherited from itk::Statistics::ProbabilityDistribution
virtual const ParametersType & GetParameters ()
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
Command * GetCommand (unsigned long tag)
bool GetDebug () const
MetaDataDictionary & GetMetaDataDictionary (void)
const MetaDataDictionary & GetMetaDataDictionary (void) const
virtual unsigned long 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
void RemoveAllObservers ()
void RemoveObserver (unsigned long tag)
void SetDebug (bool debugFlag) const
void SetMetaDataDictionary (const MetaDataDictionary &rhs)
virtual void SetReferenceCount (int)
virtual void UnRegister () 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)
static double CDF (double x, const ParametersType &)
static double CDF (double x, double mean, double variance)
static double InverseCDF (double p, const ParametersType &)
static double InverseCDF (double p, double mean, double variance)
static Pointer New ()
static double PDF (double x)
static double PDF (double x, const ParametersType &)
static double PDF (double x, double mean, double variance)
static double InverseCDF (double p)

Protected Member Functions

 GaussianDistribution (void)
void PrintSelf (std::ostream &os, Indent indent) const
virtual ~GaussianDistribution (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

 GaussianDistribution (const Self &)
void operator= (const Self &)

Additional Inherited Members

- Protected Attributes inherited from itk::Statistics::ProbabilityDistribution
ParametersType m_Parameters

Detailed Description

GaussianDistribution class defines the interface for a univariate Gaussian distribution (pdfs, cdfs, etc.).

GaussianDistribution provides access to the probability density function (pdf), the cumulative distribution function (cdf), and the inverse cumulative distribution function for a Gaussian 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.

GaussianDistributions 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).

GaussianDistributions can be used for Z-score statistical 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.
Wiki Examples:

Definition at line 60 of file itkGaussianDistribution.h.

Member Typedef Documentation

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

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 68 of file itkGaussianDistribution.h.

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

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 67 of file itkGaussianDistribution.h.

typedef GaussianDistribution itk::Statistics::GaussianDistribution::Self

Standard class typedefs

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 65 of file itkGaussianDistribution.h.

typedef ProbabilityDistribution itk::Statistics::GaussianDistribution::Superclass

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 66 of file itkGaussianDistribution.h.

Constructor & Destructor Documentation

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

Definition at line 235 of file itkGaussianDistribution.h.

itk::Statistics::GaussianDistribution::GaussianDistribution ( const Self &  )
private

Member Function Documentation

static double itk::Statistics::GaussianDistribution::CDF ( double  x)
static

Static method to evaluate the cumulative distribution function (cdf) of a standardized (mean zero, unit variance) Gaussian. The static method provides optimized access without requiring an instance of the class. Accuracy is approximately 10^-8.

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

Static method to evaluate the cumulative distribution function (cdf) of a Gaussian. The parameters of the distribution are passed as a parameter vector. The ordering of the parameters is (mean, variance). The static method provides optimized access without requiring an instance of the class.

static double itk::Statistics::GaussianDistribution::CDF ( double  x,
double  mean,
double  variance 
)
static

Static method to evaluate the cumulative distribution function (cdf) of a Gaussian. The parameters of the distribution are passed as separate values. The static method provides optimized access without requiring an instance of the class.

virtual::itk::LightObject::Pointer itk::Statistics::GaussianDistribution::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::GaussianDistribution::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::GaussianDistribution::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 (mean, variance).

Implements itk::Statistics::ProbabilityDistribution.

virtual double itk::Statistics::GaussianDistribution::EvaluateCDF ( double  x,
double  mean,
double  variance 
) const
virtual

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

virtual double itk::Statistics::GaussianDistribution::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::GaussianDistribution::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 (mean, variance).

Implements itk::Statistics::ProbabilityDistribution.

virtual double itk::Statistics::GaussianDistribution::EvaluateInverseCDF ( double  p,
double  mean,
double  variance 
) 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::GaussianDistribution::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::GaussianDistribution::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 (mean, variance).

Implements itk::Statistics::ProbabilityDistribution.

virtual double itk::Statistics::GaussianDistribution::EvaluatePDF ( double  x,
double  mean,
double  variance 
) const
virtual

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

virtual double itk::Statistics::GaussianDistribution::GetMean ( ) const
virtual

Get the mean of the Gaussian distribution. Defaults to 0.0. The mean is stored in position 0 of the parameters vector.

Implements itk::Statistics::ProbabilityDistribution.

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

Strandard macros

Reimplemented from itk::Statistics::ProbabilityDistribution.

virtual SizeValueType itk::Statistics::GaussianDistribution::GetNumberOfParameters ( ) const
inlinevirtual

Return the number of parameters. For a univariate Gaussian, this is 2 (mean, variance).

Implements itk::Statistics::ProbabilityDistribution.

Definition at line 78 of file itkGaussianDistribution.h.

virtual double itk::Statistics::GaussianDistribution::GetVariance ( ) const
virtual

Get the variance of the Gaussian distribution. Defaults to 1.0. The variance is stored in position 1 of the parameters vector.

Implements itk::Statistics::ProbabilityDistribution.

virtual bool itk::Statistics::GaussianDistribution::HasMean ( ) const
inlinevirtual

Does this distribution have a mean?

Implements itk::Statistics::ProbabilityDistribution.

Definition at line 133 of file itkGaussianDistribution.h.

virtual bool itk::Statistics::GaussianDistribution::HasVariance ( ) const
inlinevirtual

Does this distribution have a variance?

Implements itk::Statistics::ProbabilityDistribution.

Definition at line 145 of file itkGaussianDistribution.h.

static double itk::Statistics::GaussianDistribution::InverseCDF ( double  p)
static

Static method to evaluate the inverse cumulative distribution function of a standardized (mean zero, unit variance) Gaussian. The static method provides optimized access without requiring an instance of the class. Parameter p must be between 0.0 and 1.0.

THis implementation was provided by Robert W. Cox from the Biophysics Research Institute at the Medical College of Wisconsin. This function is based off of a rational polynomial approximation to the inverse Gaussian CDF which can be found in M. Abramowitz and I.A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. John Wiley & Sons. New York. Equation 26.2.23. pg. 933. 1972.

Since the initial approximation only provides an estimate within 4.5 E-4 of the true value, 3 Newton-Raphson interations are used to refine the approximation. Accuracy is approximately 10^-8.

Let, Q(x) = (1/sqrt(2*pi)) Int_{x}^{infinity} e^{-t^2/2} dt = 0.5 * erfc(x/sqrt(2))

Given p, this function computes x such that Q(x) = p, for 0 < p < 1

Note that the Gaussian CDF is defined as P(x) = (1/sqrt(2*pi)) Int_{-infinity}{x} e^{-t^2/2} dt = 1 - Q(x)

This function has been modified to compute the inverse of P(x) instead of Q(x).

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

Static method to evaluate the inverse cumulative distribution function of a Gaussian. The parameters of the distribution are passed as a parameter vector. The ordering of the parameters is (mean, variance). The static method provides optimized access without requiring an instance of the class. Parameter p must be between 0.0 and 1.0

static double itk::Statistics::GaussianDistribution::InverseCDF ( double  p,
double  mean,
double  variance 
)
static

Static method to evaluate the inverse cumulative distribution function of a Gaussian. The parameters of the distribution are passed as separate values. The static method provides optimized access without requiring an instance of the class. Parameter p must be between 0.0 and 1.0

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

Method for creation through the object factory.

Reimplemented from itk::Object.

void itk::Statistics::GaussianDistribution::operator= ( const Self &  )
private

Mutex lock to protect modification to the reference count

Reimplemented from itk::Statistics::ProbabilityDistribution.

static double itk::Statistics::GaussianDistribution::PDF ( double  x)
static

Static method to evaluate the probability density function (pdf) of a standardized (mean zero, unit variance) Gaussian. The static method provides optimized access without requiring an instance of the class.

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

Static method to evaluate the probability density function (pdf) of a Gaussian. The parameters of the distribution are passed as a parameter vector. The ordering of the parameters is (mean, variance). The static method provides optimized access without requiring an instance of the class.

static double itk::Statistics::GaussianDistribution::PDF ( double  x,
double  mean,
double  variance 
)
static

Static method to evaluate the probability density function (pdf) of a Gaussian. The parameters of the distribution are passed as separate values. The static method provides optimized access without requiring an instance of the class.

void itk::Statistics::GaussianDistribution::PrintSelf ( std::ostream &  os,
Indent  indent 
) const
protectedvirtual

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::GaussianDistribution::SetMean ( double  )
virtual

Set the mean of the Gaussian distribution. Defaults to 0.0. The mean is stored in position 0 of the parameters vector.

virtual void itk::Statistics::GaussianDistribution::SetVariance ( double  )
virtual

Set the variance of the Gaussian distribution. Defaults to 1.0. The variance is stored in position 1 of the parameters vector.

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