/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.distribution;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.apache.commons.math3.special.Beta;
import org.apache.commons.math3.special.Gamma;
/**
* Implementation of Student's t-distribution.
*
* @see "<a href='http://en.wikipedia.org/wiki/Student's_t-distribution'>Student's t-distribution (Wikipedia)</a>"
* @see "<a href='http://mathworld.wolfram.com/Studentst-Distribution.html'>Student's t-distribution (MathWorld)</a>"
*/
public class TDistribution extends AbstractRealDistribution {
/**
* Default inverse cumulative probability accuracy.
* @since 2.1
*/
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
/** Serializable version identifier */
private static final long serialVersionUID = -5852615386664158222L;
/** The degrees of freedom. */
private final double degreesOfFreedom;
/** Inverse cumulative probability accuracy. */
private final double solverAbsoluteAccuracy;
/** Static computation factor based on degreesOfFreedom. */
private final double factor;
/**
* Create a t distribution using the given degrees of freedom.
* <p>
* <b>Note:</b> this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @param degreesOfFreedom Degrees of freedom.
* @throws NotStrictlyPositiveException if {@code degreesOfFreedom <= 0}
*/
public TDistribution(double degreesOfFreedom)
throws NotStrictlyPositiveException {
this(degreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Create a t distribution using the given degrees of freedom and the
* specified inverse cumulative probability absolute accuracy.
* <p>
* <b>Note:</b> this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @param degreesOfFreedom Degrees of freedom.
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code degreesOfFreedom <= 0}
* @since 2.1
*/
public TDistribution(double degreesOfFreedom, double inverseCumAccuracy)
throws NotStrictlyPositiveException {
this(new Well19937c(), degreesOfFreedom, inverseCumAccuracy);
}
/**
* Creates a t distribution.
*
* @param rng Random number generator.
* @param degreesOfFreedom Degrees of freedom.
* @throws NotStrictlyPositiveException if {@code degreesOfFreedom <= 0}
* @since 3.3
*/
public TDistribution(RandomGenerator rng, double degreesOfFreedom)
throws NotStrictlyPositiveException {
this(rng, degreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
/**
* Creates a t distribution.
*
* @param rng Random number generator.
* @param degreesOfFreedom Degrees of freedom.
* @param inverseCumAccuracy the maximum absolute error in inverse
* cumulative probability estimates
* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
* @throws NotStrictlyPositiveException if {@code degreesOfFreedom <= 0}
* @since 3.1
*/
public TDistribution(RandomGenerator rng,
double degreesOfFreedom,
double inverseCumAccuracy)
throws NotStrictlyPositiveException {
super(rng);
if (degreesOfFreedom <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.DEGREES_OF_FREEDOM,
degreesOfFreedom);
}
this.degreesOfFreedom = degreesOfFreedom;
solverAbsoluteAccuracy = inverseCumAccuracy;
final double n = degreesOfFreedom;
final double nPlus1Over2 = (n + 1) / 2;
factor = Gamma.logGamma(nPlus1Over2) -
0.5 * (Math.log(Math.PI) + Math.log(n)) -
Gamma.logGamma(n / 2);
}
/**
* Access the degrees of freedom.
*
* @return the degrees of freedom.
*/
public double getDegreesOfFreedom() {
return degreesOfFreedom;
}
/** {@inheritDoc} */
public double density(double x) {
return Math.exp(logDensity(x));
}
/** {@inheritDoc} */
@Override
public double logDensity(double x) {
final double n = degreesOfFreedom;
final double nPlus1Over2 = (n + 1) / 2;
return factor - nPlus1Over2 * Math.log(1 + x * x / n);
}
/** {@inheritDoc} */
public double cumulativeProbability(double x) {
double ret;
if (x == 0) {
ret = 0.5;
} else {
double t =
Beta.regularizedBeta(
degreesOfFreedom / (degreesOfFreedom + (x * x)),
0.5 * degreesOfFreedom,
0.5);
if (x < 0.0) {
ret = 0.5 * t;
} else {
ret = 1.0 - 0.5 * t;
}
}
return ret;
}
/** {@inheritDoc} */
@Override
protected double getSolverAbsoluteAccuracy() {
return solverAbsoluteAccuracy;
}
/**
* {@inheritDoc}
*
* For degrees of freedom parameter {@code df}, the mean is
* <ul>
* <li>if {@code df > 1} then {@code 0},</li>
* <li>else undefined ({@code Double.NaN}).</li>
* </ul>
*/
public double getNumericalMean() {
final double df = getDegreesOfFreedom();
if (df > 1) {
return 0;
}
return Double.NaN;
}
/**
* {@inheritDoc}
*
* For degrees of freedom parameter {@code df}, the variance is
* <ul>
* <li>if {@code df > 2} then {@code df / (df - 2)},</li>
* <li>if {@code 1 < df <= 2} then positive infinity
* ({@code Double.POSITIVE_INFINITY}),</li>
* <li>else undefined ({@code Double.NaN}).</li>
* </ul>
*/
public double getNumericalVariance() {
final double df = getDegreesOfFreedom();
if (df > 2) {
return df / (df - 2);
}
if (df > 1 && df <= 2) {
return Double.POSITIVE_INFINITY;
}
return Double.NaN;
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always negative infinity no matter the
* parameters.
*
* @return lower bound of the support (always
* {@code Double.NEGATIVE_INFINITY})
*/
public double getSupportLowerBound() {
return Double.NEGATIVE_INFINITY;
}
/**
* {@inheritDoc}
*
* The upper bound of the support is always positive infinity no matter the
* parameters.
*
* @return upper bound of the support (always
* {@code Double.POSITIVE_INFINITY})
*/
public double getSupportUpperBound() {
return Double.POSITIVE_INFINITY;
}
/** {@inheritDoc} */
public boolean isSupportLowerBoundInclusive() {
return false;
}
/** {@inheritDoc} */
public boolean isSupportUpperBoundInclusive() {
return false;
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
}