gov.sandia.cognition.statistics.distribution

Class StudentTDistribution

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.statistics.AbstractDistribution<NumberType>

gov.sandia.cognition.statistics.AbstractClosedFormUnivariateDistribution<java.lang.Double>

gov.sandia.cognition.statistics.AbstractClosedFormSmoothUnivariateDistribution

gov.sandia.cognition.statistics.distribution.StudentTDistribution

All Implemented Interfaces:

Vectorizable, ClosedFormComputableDistribution<java.lang.Double>, ClosedFormDistribution<java.lang.Double>, ClosedFormUnivariateDistribution<java.lang.Double>, ComputableDistribution<java.lang.Double>, Distribution<java.lang.Double>, DistributionWithMean<java.lang.Double>, EstimableDistribution<java.lang.Double,StudentTDistribution>, SmoothUnivariateDistribution, UnivariateDistribution<java.lang.Double>, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

Direct Known Subclasses:

StudentTDistribution.CDF, StudentTDistribution.PDF

@PublicationReference(author="Christopher Bishop",title="Pattern Recognition and Machine Learning",type=Book,year=2006,pages={102,105}) @PublicationReference(author="Wikipedia",title="Student\'s t-distribution",type=WebPage,year=2009,url="http://en.wikipedia.org/wiki/Student_t_distribution")
public class StudentTDistribution
extends AbstractClosedFormSmoothUnivariateDistribution
implements EstimableDistribution<java.lang.Double,StudentTDistribution>

Defines a noncentral Student-t Distribution.

Since:

2.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	StudentTDistribution.CDF Evaluator that computes the Cumulative Distribution Function (CDF) of a Student-t distribution with a fixed number of degrees of freedom
static class	StudentTDistribution.MaximumLikelihoodEstimator Estimates the parameters of the Student-t distribution from the given data, where the degrees of freedom are estimated from the Kurtosis of the sample data.
static class	StudentTDistribution.PDF Evaluator that computes the Probability Density Function (CDF) of a Student-t distribution with a fixed number of degrees of freedom
static class	StudentTDistribution.WeightedMaximumLikelihoodEstimator Creates a UnivariateGaussian from weighted data

Field Summary

Fields

Modifier and Type	Field and Description
static double	DEFAULT_DEGREES_OF_FREEDOM Default degrees of freedom, 3.0.
static double	DEFAULT_MEAN Default mean, 0.0.
static double	DEFAULT_PRECISION Default precision, 1.0.
protected double	degreesOfFreedom Degrees of freedom in the distribution, usually the number of datapoints - 1, DOFs must be greater than zero.
protected double	mean Mean, or noncentrality parameter, of the distribution
protected double	precision Precision, which is proportionate to the inverseRootFinder of variance, of the distribution, must be greater than zero.

Constructor Summary

Constructors

Constructor and Description
StudentTDistribution() Default degrees of freedom.
StudentTDistribution(double degreesOfFreedom) Creates a new instance of StudentTDistribution
StudentTDistribution(double degreesOfFreedom, double mean, double precision) Creates a new instance of StudentTDistribution
StudentTDistribution(StudentTDistribution other) Copy constructor

Method Summary

Modifier and Type	Method and Description
StudentTDistribution	clone() This makes public the clone method on the Object class and removes the exception that it throws.
void	convertFromVector(Vector parameters) Sets the parameters of this PDF, which must be a 1-dimensional Vector containing the degrees of freedom
Vector	convertToVector() Returns the parameters of this PDF, which is a 1-dimensional Vector containing the degrees of freedom
StudentTDistribution.CDF	getCDF() Gets the CDF of a scalar distribution.
double	getDegreesOfFreedom() Getter for degreesOfFreedom
StudentTDistribution.MaximumLikelihoodEstimator	getEstimator() Gets an estimator associated with this distribution.
java.lang.Double	getMaxSupport() Gets the minimum support (domain or input) of the distribution.
double	getMeanAsDouble() Gets the mean of the distribution as a double.
java.lang.Double	getMinSupport() Gets the minimum support (domain or input) of the distribution.
double	getPrecision() Getter for precision
StudentTDistribution.PDF	getProbabilityFunction() Gets the distribution function associated with this Distribution, either the PDF or PMF.
double	getVariance() Gets the variance of the distribution.
void	sampleInto(java.util.Random random, double[] output, int start, int length) Samples values from this distribution as an array of doubles.
void	setDegreesOfFreedom(double degreesOfFreedom) Setter for degreesOfFreedom
void	setMean(double mean) Setter for mean
void	setPrecision(double precision) Setter for precision
java.lang.String	toString()

Methods inherited from class gov.sandia.cognition.statistics.AbstractClosedFormSmoothUnivariateDistribution

getMean, sampleAsDouble, sampleAsDoubles, sampleInto

Methods inherited from class gov.sandia.cognition.statistics.AbstractDistribution

sample, sample

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface gov.sandia.cognition.statistics.Distribution

sample, sample, sampleInto

Field Detail

DEFAULT_DEGREES_OF_FREEDOM

public static final double DEFAULT_DEGREES_OF_FREEDOM

Default degrees of freedom, 3.0.

See Also:

Constant Field Values

DEFAULT_MEAN

public static final double DEFAULT_MEAN

Default mean, 0.0.

See Also:

Constant Field Values

DEFAULT_PRECISION

public static final double DEFAULT_PRECISION

Default precision, 1.0.

See Also:

Constant Field Values

precision

protected double precision

Precision, which is proportionate to the inverseRootFinder of variance, of the distribution, must be greater than zero. Note that we are using "precision" instead of "variance" because the variance of the Student-t has another scale factor based on the dofs and we want to avoid confusion.

mean

protected double mean

Mean, or noncentrality parameter, of the distribution

degreesOfFreedom

protected double degreesOfFreedom

Degrees of freedom in the distribution, usually the number of datapoints - 1, DOFs must be greater than zero.

Constructor Detail

StudentTDistribution

public StudentTDistribution()

Default degrees of freedom.

StudentTDistribution

public StudentTDistribution(double degreesOfFreedom)

Creates a new instance of StudentTDistribution

Parameters:

degreesOfFreedom - Degrees of freedom in the distribution, usually the number of datapoints - 1, DOFs must be greater than zero.

StudentTDistribution

public StudentTDistribution(double degreesOfFreedom,
                            double mean,
                            double precision)

Creates a new instance of StudentTDistribution

Parameters:

degreesOfFreedom - Degrees of freedom in the distribution, usually the number of datapoints - 1, DOFs must be greater than zero.

mean - Mean, or noncentrality parameter, of the distribution

precision - Precision, inverseRootFinder variance, of the distribution, must be greater than zero.

StudentTDistribution

public StudentTDistribution(StudentTDistribution other)

Copy constructor

Parameters:

other - StudentTDistribution to copy

Method Detail

clone

public StudentTDistribution clone()

Description copied from class: AbstractCloneableSerializable

This makes public the clone method on the Object class and removes the exception that it throws. Its default behavior is to automatically create a clone of the exact type of object that the clone is called on and to copy all primitives but to keep all references, which means it is a shallow copy. Extensions of this class may want to override this method (but call super.clone() to implement a "smart copy". That is, to target the most common use case for creating a copy of the object. Because of the default behavior being a shallow copy, extending classes only need to handle fields that need to have a deeper copy (or those that need to be reset). Some of the methods in ObjectUtil may be helpful in implementing a custom clone method. Note: The contract of this method is that you must use super.clone() as the basis for your implementation.

Specified by:

clone in interface Vectorizable

Specified by:

clone in interface CloneableSerializable

Overrides:

clone in class AbstractClosedFormUnivariateDistribution<java.lang.Double>

Returns:

A clone of this object.

getDegreesOfFreedom

public double getDegreesOfFreedom()

Getter for degreesOfFreedom

Returns:

Degrees of freedom in the distribution, usually the number of datapoints - 1, DOFs must be greater than zero.

setDegreesOfFreedom

public void setDegreesOfFreedom(double degreesOfFreedom)

Setter for degreesOfFreedom

Parameters:

degreesOfFreedom - Degrees of freedom in the distribution, usually the number of datapoints - 1, DOFs must be greater than zero.

getVariance

public double getVariance()

Description copied from interface: UnivariateDistribution

Gets the variance of the distribution. This is sometimes called the second central moment by more pedantic people, which is equivalent to the square of the standard deviation.

Specified by:

getVariance in interface UnivariateDistribution<java.lang.Double>

Returns:

Variance of the distribution.

convertToVector

public Vector convertToVector()

Returns the parameters of this PDF, which is a 1-dimensional Vector containing the degrees of freedom

Specified by:

convertToVector in interface Vectorizable

Returns:

1-dimensional Vector containing the degrees of freedom

convertFromVector

public void convertFromVector(Vector parameters)

Sets the parameters of this PDF, which must be a 1-dimensional Vector containing the degrees of freedom

Specified by:

convertFromVector in interface Vectorizable

Parameters:

parameters - 1-dimensional Vector containing the degrees of freedom

sampleInto

public void sampleInto(java.util.Random random,
                       double[] output,
                       int start,
                       int length)

Description copied from interface: SmoothUnivariateDistribution

Samples values from this distribution as an array of doubles. This is a convenience method to potentially avoid boxing.

Specified by:

sampleInto in interface SmoothUnivariateDistribution

Parameters:

random - Random number generator to use.

output - The array to write the result into. Cannot be null.

start - The offset in the array to start writing at. Cannot be negative.

length - The number of values to sample. Cannot be negative.

getCDF

public StudentTDistribution.CDF getCDF()

Description copied from interface: UnivariateDistribution

Gets the CDF of a scalar distribution.

Specified by:

getCDF in interface ClosedFormUnivariateDistribution<java.lang.Double>

Specified by:

getCDF in interface SmoothUnivariateDistribution

Specified by:

getCDF in interface UnivariateDistribution<java.lang.Double>

Returns:

CDF of the scalar distribution.

getProbabilityFunction

public StudentTDistribution.PDF getProbabilityFunction()

Description copied from interface: ComputableDistribution

Gets the distribution function associated with this Distribution, either the PDF or PMF.

Specified by:

getProbabilityFunction in interface ComputableDistribution<java.lang.Double>

Specified by:

getProbabilityFunction in interface SmoothUnivariateDistribution

Returns:

Distribution function associated with this Distribution.

getPrecision

public double getPrecision()

Getter for precision

Returns:

Precision, inverseRootFinder variance, of the distribution, must be greater than zero.

setPrecision

public void setPrecision(double precision)

Setter for precision

Parameters:

precision - Precision, inverseRootFinder variance, of the distribution, must be greater than zero.

setMean

public void setMean(double mean)

Setter for mean

Parameters:

mean - Mean, or noncentrality parameter, of the distribution

getMeanAsDouble

public double getMeanAsDouble()

Description copied from interface: UnivariateDistribution

Gets the mean of the distribution as a double.

Specified by:

getMeanAsDouble in interface UnivariateDistribution<java.lang.Double>

Returns:

The mean as a double.

getMinSupport

public java.lang.Double getMinSupport()

Description copied from interface: UnivariateDistribution

Gets the minimum support (domain or input) of the distribution.

Specified by:

getMinSupport in interface UnivariateDistribution<java.lang.Double>

Returns:

Minimum support.

getMaxSupport

public java.lang.Double getMaxSupport()

Description copied from interface: UnivariateDistribution

Gets the minimum support (domain or input) of the distribution.

Specified by:

getMaxSupport in interface UnivariateDistribution<java.lang.Double>

Returns:

Minimum support.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

getEstimator

public StudentTDistribution.MaximumLikelihoodEstimator getEstimator()

Description copied from interface: EstimableDistribution

Gets an estimator associated with this distribution.

Specified by:

getEstimator in interface EstimableDistribution<java.lang.Double,StudentTDistribution>

Returns:

A distribution estimator associated for this distribution.