Package jsl.utilities.distributions

Class StudentT

java.lang.Object

jsl.utilities.distributions.Distribution

jsl.utilities.distributions.StudentT

All Implemented Interfaces:

ControllableIfc, CDFIfc, ContinuousDistributionIfc, DistributionFunctionIfc, DistributionIfc, DomainIfc, InverseCDFIfc, MeanIfc, PDFIfc, VarianceIfc, GetNameIfc, IdentityIfc, NewInstanceIfc, ParametersIfc, GetRVariableIfc

public class StudentT
extends Distribution
implements ContinuousDistributionIfc, InverseCDFIfc, GetRVariableIfc

The Student T distribution See http://www.mth.kcl.ac.uk/~shaww/web_page/papers/Tdistribution06.pdf See http://en.wikipedia.org/wiki/Student's_t-distribution This implementation limits the degrees of freedom to be greater than or equal to 1.0 Bailey's acceptance rejection is used for sampling by default but inverse transform can be selected

Nested Class Summary

Nested classes/interfaces inherited from class jsl.utilities.distributions.Distribution

Distribution.RandomControls

Field Summary

Fields

Modifier and Type	Field	Description
static StudentT	defaultT	A default instance for easily computing Student-T values

Fields inherited from class jsl.utilities.distributions.Distribution

myId, myName

Constructor Summary

Constructors

Constructor	Description
StudentT()	Constructs a StudentT distribution with 1.0 degree of freedom
StudentT(double dof)	Constructs a StudentT distribution dof degrees of freedom
StudentT(double[] parameters)	Constructs a StudentT distribution with parameters[0] = degrees of freedom
StudentT(double dof, java.lang.String name)	Constructs a StudentT distribution dof degrees of freedom

Method Summary

Modifier and Type	Method	Description
double	cdf(double x)	Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function
static double	getCDF(double dof, double x)	A convenience method that uses defaultT to return the value of the CDF at the supplied x This method has the side effect of changing the degrees of freedom defaultT
double	getDegreesOfFreedom()
Interval	getDomain()
double	getIntervalFactor()	Used in the binary search to set the search interval for the inverse CDF.
static double	getInvCDF(double dof, double p)	A convenience method that uses defaultT to return the value of the inverse CDF at the supplied p This method has the side effect of changing the degrees of freedom for defaultT
double	getMean()	Returns the mean or expected value of a distribution
double[]	getParameters()	Gets the parameters
RVariableIfc	getRandomVariable(RNStreamIfc rng)
double	getVariance()	Returns the variance of the distribution if defined
double	invCDF(double p)	Provides the inverse cumulative distribution function for the distribution While closed form solutions for the inverse cdf may not exist, numerical search methods can be used to solve F(X) = U.
StudentT	newInstance()	Returns a new instance
double	pdf(double x)	Returns the f(x) where f represents the probability density function for the distribution.
void	setDegreesOfFreedom(double dof)	Sets the degrees of freedom for the distribution
void	setIntervalFactor(double factor)	Used in the binary search to set the search interval for the inverse CDF.
void	setParameters(double[] parameters)	Sets the parameters

Methods inherited from class jsl.utilities.distributions.Distribution

getControls, getId, getName, getStandardDeviation, inverseContinuousCDFViaBisection, inverseContinuousCDFViaBisection, inverseDiscreteCDFViaSearchUp, setControls, setId, setName, toString

Methods inherited from class java.lang.Object

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

Methods inherited from interface jsl.utilities.distributions.CDFIfc

cdf, complementaryCDF

Methods inherited from interface jsl.utilities.random.rvariable.GetRVariableIfc

getRandomVariable, getRandomVariable

Field Detail

defaultT

public static final StudentT defaultT

A default instance for easily computing Student-T values

Constructor Detail

StudentT

public StudentT()

Constructs a StudentT distribution with 1.0 degree of freedom

StudentT

public StudentT(double[] parameters)

Constructs a StudentT distribution with parameters[0] = degrees of freedom

Parameters:

parameters - An array with the degrees of freedom

StudentT

public StudentT(double dof)

Constructs a StudentT distribution dof degrees of freedom

Parameters:

dof - degrees of freedom

StudentT

public StudentT(double dof,
                java.lang.String name)

Constructs a StudentT distribution dof degrees of freedom

Parameters:

dof - degrees of freedom

name - an optional name/label

Method Detail

newInstance

public final StudentT newInstance()

Description copied from interface: NewInstanceIfc

Returns a new instance

Specified by:

newInstance in interface NewInstanceIfc

Specified by:

newInstance in class Distribution

Returns:

the new instance

getDomain

public final Interval getDomain()

Specified by:

getDomain in interface DomainIfc

setDegreesOfFreedom

public final void setDegreesOfFreedom(double dof)

Sets the degrees of freedom for the distribution

Parameters:

dof - must be >= 1.0

getDegreesOfFreedom

public final double getDegreesOfFreedom()

Returns:

the degrees of freedom

getIntervalFactor

public final double getIntervalFactor()

Used in the binary search to set the search interval for the inverse CDF. The default addFactor is 6.0 The interval will be: start = Normal.stdNormalInvCDF(p) ll = start - getIntervalFactor()*getStandardDeviation(); ul = start + getIntervalFactor()*getStandardDeviation();

Returns:

the factor

setIntervalFactor

public final void setIntervalFactor(double factor)

Used in the binary search to set the search interval for the inverse CDF. The default addFactor is 6.0 The interval will be: start = Normal.stdNormalInvCDF(p) ll = start - getIntervalFactor()*getStandardDeviation(); ul = start + getIntervalFactor()*getStandardDeviation();

Parameters:

factor - the factor

setParameters

public void setParameters(double[] parameters)

Description copied from interface: ParametersIfc

Sets the parameters

Specified by:

setParameters in interface ParametersIfc

Parameters:

parameters - an array of doubles representing the parameters

getParameters

public double[] getParameters()

Description copied from interface: ParametersIfc

Gets the parameters

Specified by:

getParameters in interface ParametersIfc

Returns:

Returns an array of the parameters

getMean

public double getMean()

Description copied from interface: MeanIfc

Returns the mean or expected value of a distribution

Specified by:

getMean in interface MeanIfc

Returns:

double the mean or expected value for the distribution

getVariance

public double getVariance()

Description copied from interface: VarianceIfc

Returns the variance of the distribution if defined

Specified by:

getVariance in interface VarianceIfc

Returns:

double the variance of the random variable

pdf

public double pdf(double x)

Description copied from interface: PDFIfc

Returns the f(x) where f represents the probability density function for the distribution. Note this is not a probability.

Specified by:

pdf in interface PDFIfc

Parameters:

x - a double representing the value to be evaluated

Returns:

f(x)

getCDF

public static double getCDF(double dof,
                            double x)

A convenience method that uses defaultT to return the value of the CDF at the supplied x This method has the side effect of changing the degrees of freedom defaultT

Parameters:

dof - the degrees of freedom

x - the value to evaluate

Returns:

the CDF value

getInvCDF

public static double getInvCDF(double dof,
                               double p)

A convenience method that uses defaultT to return the value of the inverse CDF at the supplied p This method has the side effect of changing the degrees of freedom for defaultT

Parameters:

dof - the degrees of freedom

p - the value to evaluate

Returns:

the inverse

cdf

public double cdf(double x)

Description copied from interface: CDFIfc

Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function

Specified by:

cdf in interface CDFIfc

Parameters:

x - a double representing the upper limit

Returns:

a double representing the probability

invCDF

public double invCDF(double p)

Description copied from interface: InverseCDFIfc

Provides the inverse cumulative distribution function for the distribution While closed form solutions for the inverse cdf may not exist, numerical search methods can be used to solve F(X) = U.

Specified by:

invCDF in interface InverseCDFIfc

Parameters:

p - The probability to be evaluated for the inverse, p must be [0,1] or an IllegalArgumentException is thrown

Returns:

The inverse cdf evaluated at the supplied probability

getRandomVariable

public final RVariableIfc getRandomVariable(RNStreamIfc rng)

Specified by:

getRandomVariable in interface GetRVariableIfc

Overrides:

getRandomVariable in class Distribution

Parameters:

rng - the stream to use

Returns:

a random variable