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Diffstat (limited to 'src/main/java/org/apache/commons/math3/distribution/TDistribution.java')
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1 files changed, 270 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/distribution/TDistribution.java b/src/main/java/org/apache/commons/math3/distribution/TDistribution.java new file mode 100644 index 0000000..8e6053a --- /dev/null +++ b/src/main/java/org/apache/commons/math3/distribution/TDistribution.java @@ -0,0 +1,270 @@ +/* + * 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; +import org.apache.commons.math3.util.FastMath; + +/** + * 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 * (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} + * + * <p>For degrees of freedom parameter {@code df}, the mean is + * + * <ul> + * <li>if {@code df > 1} then {@code 0}, + * <li>else undefined ({@code Double.NaN}). + * </ul> + */ + public double getNumericalMean() { + final double df = getDegreesOfFreedom(); + + if (df > 1) { + return 0; + } + + return Double.NaN; + } + + /** + * {@inheritDoc} + * + * <p>For degrees of freedom parameter {@code df}, the variance is + * + * <ul> + * <li>if {@code df > 2} then {@code df / (df - 2)}, + * <li>if {@code 1 < df <= 2} then positive infinity ({@code Double.POSITIVE_INFINITY}), + * <li>else undefined ({@code Double.NaN}). + * </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} + * + * <p>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} + * + * <p>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} + * + * <p>The support of this distribution is connected. + * + * @return {@code true} + */ + public boolean isSupportConnected() { + return true; + } +} |