Java tutorial
/* * 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.special.Beta; import org.apache.commons.math3.special.Gamma; import org.apache.commons.math3.util.FastMath; import org.apache.commons.math3.random.RandomGenerator; import org.apache.commons.math3.random.Well19937c; /** * 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>" * @version $Id: TDistribution.java 1416643 2012-12-03 19:37:14Z tn $ */ 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; /** * Create a t distribution using the given degrees of freedom. * * @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. * * @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. * @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; } /** * Access the degrees of freedom. * * @return the degrees of freedom. */ public double getDegreesOfFreedom() { return degreesOfFreedom; } /** {@inheritDoc} */ public double density(double x) { final double n = degreesOfFreedom; final double nPlus1Over2 = (n + 1) / 2; return FastMath.exp(Gamma.logGamma(nPlus1Over2) - 0.5 * (FastMath.log(FastMath.PI) + FastMath.log(n)) - Gamma.logGamma(n / 2) - 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; } }