jidt/java/source/infodynamics/utils/commonsmath3/distribution/TDistribution.java

/*
 *  Java Information Dynamics Toolkit (JIDT)
 *  Copyright (C) 2017, Joseph T. Lizier
 *  
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *  
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *  
 *  You should have received a copy of the GNU General Public License
 *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/

/*
 * This class was originally distributed as part of the Apache Commons
 *  Math3 library (3.6.1), under the Apache License Version 2.0, which is 
 *  copied below. This Apache 2 software is now included as a derivative
 *  work in the GPLv3 licensed JIDT project, as per:
 *  http://www.apache.org/licenses/GPL-compatibility.html
 *  
 * The original Apache source code has been modified as follows:
 * -- We have modified package names to sit inside the JIDT structure.
 */

/*
 * 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 infodynamics.utils.commonsmath3.distribution;

import infodynamics.utils.commonsmath3.exception.NotStrictlyPositiveException;
import infodynamics.utils.commonsmath3.exception.util.LocalizedFormats;
import infodynamics.utils.commonsmath3.random.RandomGenerator;
import infodynamics.utils.commonsmath3.random.Well19937c;
import infodynamics.utils.commonsmath3.special.Beta;
import infodynamics.utils.commonsmath3.special.Gamma;
import infodynamics.utils.commonsmath3.util.FastMath;

/**
 * Implementation of Student's t-distribution.
 *
 * @see "<a href='http://en.wikipedia.org/wiki/Student&apos;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 * (FastMath.log(FastMath.PI) + FastMath.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 FastMath.exp(logDensity(x));
    }

    /** {@inheritDoc} */
    @Override
    public double logDensity(double x) {
        final double n = degreesOfFreedom;
        final double nPlus1Over2 = (n + 1) / 2;
        return factor - nPlus1Over2 * FastMath.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;
    }
}