org.apache.commons.math3.distribution

Class TDistribution

java.lang.Object

org.apache.commons.math3.distribution.AbstractRealDistribution

org.apache.commons.math3.distribution.TDistribution

All Implemented Interfaces:

java.io.Serializable, RealDistribution

public class TDistribution
extends AbstractRealDistribution

Implementation of Student's t-distribution.

See Also:

"Student's t-distribution (Wikipedia)", "Student's t-distribution (MathWorld)", Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static double	DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy.
private double	degreesOfFreedom The degrees of freedom.
private double	factor Static computation factor based on degreesOfFreedom.
private static long	serialVersionUID Serializable version identifier
private double	solverAbsoluteAccuracy Inverse cumulative probability accuracy.

Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

Constructors

Constructor and Description
TDistribution(double degreesOfFreedom) Create a t distribution using the given degrees of freedom.
TDistribution(double degreesOfFreedom, double inverseCumAccuracy) Create a t distribution using the given degrees of freedom and the specified inverse cumulative probability absolute accuracy.
TDistribution(RandomGenerator rng, double degreesOfFreedom) Creates a t distribution.
TDistribution(RandomGenerator rng, double degreesOfFreedom, double inverseCumAccuracy) Creates a t distribution.

Method Summary

Methods

Modifier and Type	Method and Description
double	cumulativeProbability(double x) For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double	density(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
double	getDegreesOfFreedom() Access the degrees of freedom.
double	getNumericalMean() Use this method to get the numerical value of the mean of this distribution.
double	getNumericalVariance() Use this method to get the numerical value of the variance of this distribution.
protected double	getSolverAbsoluteAccuracy() Returns the solver absolute accuracy for inverse cumulative computation.
double	getSupportLowerBound() Access the lower bound of the support.
double	getSupportUpperBound() Access the upper bound of the support.
boolean	isSupportConnected() Use this method to get information about whether the support is connected, i.e.
boolean	isSupportLowerBoundInclusive() Whether or not the lower bound of support is in the domain of the density function.
boolean	isSupportUpperBoundInclusive() Whether or not the upper bound of support is in the domain of the density function.
double	logDensity(double x) Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.

Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

cumulativeProbability, inverseCumulativeProbability, probability, probability, reseedRandomGenerator, sample, sample

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Default inverse cumulative probability accuracy.

Since:

2.1

See Also:

Constant Field Values

serialVersionUID

private static final long serialVersionUID

Serializable version identifier

See Also:

Constant Field Values

degreesOfFreedom

private final double degreesOfFreedom

The degrees of freedom.

solverAbsoluteAccuracy

private final double solverAbsoluteAccuracy

Inverse cumulative probability accuracy.

factor

private final double factor

Static computation factor based on degreesOfFreedom.

Constructor Detail

TDistribution

public TDistribution(double degreesOfFreedom)
              throws NotStrictlyPositiveException

Create a t distribution using the given degrees of freedom.

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

Parameters:

degreesOfFreedom - Degrees of freedom.

Throws:

NotStrictlyPositiveException - if degreesOfFreedom <= 0

TDistribution

public TDistribution(double degreesOfFreedom,
             double inverseCumAccuracy)
              throws NotStrictlyPositiveException

Create a t distribution using the given degrees of freedom and the specified inverse cumulative probability absolute accuracy.

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

Parameters:

degreesOfFreedom - Degrees of freedom.

inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).

Throws:

NotStrictlyPositiveException - if degreesOfFreedom <= 0

Since:

2.1

TDistribution

public TDistribution(RandomGenerator rng,
             double degreesOfFreedom)
              throws NotStrictlyPositiveException

Creates a t distribution.

Parameters:

rng - Random number generator.

degreesOfFreedom - Degrees of freedom.

Throws:

NotStrictlyPositiveException - if degreesOfFreedom <= 0

Since:

3.3

TDistribution

public TDistribution(RandomGenerator rng,
             double degreesOfFreedom,
             double inverseCumAccuracy)
              throws NotStrictlyPositiveException

Creates a t distribution.

Parameters:

rng - Random number generator.

degreesOfFreedom - Degrees of freedom.

inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).

Throws:

NotStrictlyPositiveException - if degreesOfFreedom <= 0

Since:

3.1

Method Detail

getDegreesOfFreedom

public double getDegreesOfFreedom()

Access the degrees of freedom.

Returns:

the degrees of freedom.

density

public double density(double x)

Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.

Parameters:

x - the point at which the PDF is evaluated

Returns:

the value of the probability density function at point x

logDensity

public double logDensity(double x)

Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of RealDistribution.density(double). The default implementation simply computes the logarithm of density(x).

Overrides:

logDensity in class AbstractRealDistribution

Parameters:

x - the point at which the PDF is evaluated

Returns:

the logarithm of the value of the probability density function at point x

cumulativeProbability

public double cumulativeProbability(double x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.

Parameters:

x - the point at which the CDF is evaluated

Returns:

the probability that a random variable with this distribution takes a value less than or equal to x

getSolverAbsoluteAccuracy

protected double getSolverAbsoluteAccuracy()

Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

Overrides:

getSolverAbsoluteAccuracy in class AbstractRealDistribution

Returns:

the maximum absolute error in inverse cumulative probability estimates

getNumericalMean

public double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution. For degrees of freedom parameter df, the mean is

• if df > 1 then 0,
• else undefined (Double.NaN).

Returns:

the mean or Double.NaN if it is not defined

getNumericalVariance

public double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution. For degrees of freedom parameter df, the variance is

• if df > 2 then df / (df - 2),
• if 1 < df <= 2 then positive infinity (Double.POSITIVE_INFINITY),
• else undefined (Double.NaN).

Returns:

the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

getSupportLowerBound

public double getSupportLowerBound()

Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X <= x) > 0}.

The lower bound of the support is always negative infinity no matter the parameters.

Returns:

lower bound of the support (always Double.NEGATIVE_INFINITY)

getSupportUpperBound

public double getSupportUpperBound()

Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

The upper bound of the support is always positive infinity no matter the parameters.

Returns:

upper bound of the support (always Double.POSITIVE_INFINITY)

isSupportLowerBoundInclusive

public boolean isSupportLowerBoundInclusive()

Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

Returns:

true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()

Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

Returns:

true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportConnected

public boolean isSupportConnected()

Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.

Returns:

true