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.NumberIsTooLargeException; import org.apache.commons.math3.exception.NumberIsTooSmallException; import org.apache.commons.math3.exception.OutOfRangeException; import org.apache.commons.math3.exception.util.LocalizedFormats; import org.apache.commons.math3.util.FastMath; import org.apache.commons.math3.random.RandomGenerator; import org.apache.commons.math3.random.Well19937c; /** * Implementation of the triangular real distribution. * * @see <a href="http://en.wikipedia.org/wiki/Triangular_distribution"> * Triangular distribution (Wikipedia)</a> * * @version $Id: TriangularDistribution.java 1416643 2012-12-03 19:37:14Z tn $ * @since 3.0 */ public class TriangularDistribution extends AbstractRealDistribution { /** Serializable version identifier. */ private static final long serialVersionUID = 20120112L; /** Lower limit of this distribution (inclusive). */ private final double a; /** Upper limit of this distribution (inclusive). */ private final double b; /** Mode of this distribution. */ private final double c; /** Inverse cumulative probability accuracy. */ private final double solverAbsoluteAccuracy; /** * Creates a triangular real distribution using the given lower limit, * upper limit, and mode. * * @param a Lower limit of this distribution (inclusive). * @param b Upper limit of this distribution (inclusive). * @param c Mode of this distribution. * @throws NumberIsTooLargeException if {@code a >= b} or if {@code c > b}. * @throws NumberIsTooSmallException if {@code c < a}. */ public TriangularDistribution(double a, double c, double b) throws NumberIsTooLargeException, NumberIsTooSmallException { this(new Well19937c(), a, c, b); } /** * Creates a triangular distribution. * * @param rng Random number generator. * @param a Lower limit of this distribution (inclusive). * @param b Upper limit of this distribution (inclusive). * @param c Mode of this distribution. * @throws NumberIsTooLargeException if {@code a >= b} or if {@code c > b}. * @throws NumberIsTooSmallException if {@code c < a}. * @since 3.1 */ public TriangularDistribution(RandomGenerator rng, double a, double c, double b) throws NumberIsTooLargeException, NumberIsTooSmallException { super(rng); if (a >= b) { throw new NumberIsTooLargeException(LocalizedFormats.LOWER_BOUND_NOT_BELOW_UPPER_BOUND, a, b, false); } if (c < a) { throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_TOO_SMALL, c, a, true); } if (c > b) { throw new NumberIsTooLargeException(LocalizedFormats.NUMBER_TOO_LARGE, c, b, true); } this.a = a; this.c = c; this.b = b; solverAbsoluteAccuracy = FastMath.max(FastMath.ulp(a), FastMath.ulp(b)); } /** * Returns the mode {@code c} of this distribution. * * @return the mode {@code c} of this distribution */ public double getMode() { return c; } /** * {@inheritDoc} * * <p> * For this distribution, the returned value is not really meaningful, * since exact formulas are implemented for the computation of the * {@link #inverseCumulativeProbability(double)} (no solver is invoked). * </p> * <p> * For lower limit {@code a} and upper limit {@code b}, the current * implementation returns {@code max(ulp(a), ulp(b)}. * </p> */ @Override protected double getSolverAbsoluteAccuracy() { return solverAbsoluteAccuracy; } /** * {@inheritDoc} * * For lower limit {@code a}, upper limit {@code b} and mode {@code c}, the * PDF is given by * <ul> * <li>{@code 2 * (x - a) / [(b - a) * (c - a)]} if {@code a <= x < c},</li> * <li>{@code 2 / (b - a)} if {@code x = c},</li> * <li>{@code 2 * (b - x) / [(b - a) * (b - c)]} if {@code c < x <= b},</li> * <li>{@code 0} otherwise. * </ul> */ public double density(double x) { if (x < a) { return 0; } if (a <= x && x < c) { double divident = 2 * (x - a); double divisor = (b - a) * (c - a); return divident / divisor; } if (x == c) { return 2 / (b - a); } if (c < x && x <= b) { double divident = 2 * (b - x); double divisor = (b - a) * (b - c); return divident / divisor; } return 0; } /** * {@inheritDoc} * * For lower limit {@code a}, upper limit {@code b} and mode {@code c}, the * CDF is given by * <ul> * <li>{@code 0} if {@code x < a},</li> * <li>{@code (x - a)^2 / [(b - a) * (c - a)]} if {@code a <= x < c},</li> * <li>{@code (c - a) / (b - a)} if {@code x = c},</li> * <li>{@code 1 - (b - x)^2 / [(b - a) * (b - c)]} if {@code c < x <= b},</li> * <li>{@code 1} if {@code x > b}.</li> * </ul> */ public double cumulativeProbability(double x) { if (x < a) { return 0; } if (a <= x && x < c) { double divident = (x - a) * (x - a); double divisor = (b - a) * (c - a); return divident / divisor; } if (x == c) { return (c - a) / (b - a); } if (c < x && x <= b) { double divident = (b - x) * (b - x); double divisor = (b - a) * (b - c); return 1 - (divident / divisor); } return 1; } /** * {@inheritDoc} * * For lower limit {@code a}, upper limit {@code b}, and mode {@code c}, * the mean is {@code (a + b + c) / 3}. */ public double getNumericalMean() { return (a + b + c) / 3; } /** * {@inheritDoc} * * For lower limit {@code a}, upper limit {@code b}, and mode {@code c}, * the variance is {@code (a^2 + b^2 + c^2 - a * b - a * c - b * c) / 18}. */ public double getNumericalVariance() { return (a * a + b * b + c * c - a * b - a * c - b * c) / 18; } /** * {@inheritDoc} * * The lower bound of the support is equal to the lower limit parameter * {@code a} of the distribution. * * @return lower bound of the support */ public double getSupportLowerBound() { return a; } /** * {@inheritDoc} * * The upper bound of the support is equal to the upper limit parameter * {@code b} of the distribution. * * @return upper bound of the support */ public double getSupportUpperBound() { return b; } /** {@inheritDoc} */ public boolean isSupportLowerBoundInclusive() { return true; } /** {@inheritDoc} */ public boolean isSupportUpperBoundInclusive() { return true; } /** * {@inheritDoc} * * The support of this distribution is connected. * * @return {@code true} */ public boolean isSupportConnected() { return true; } @Override public double inverseCumulativeProbability(double p) throws OutOfRangeException { if (p < 0 || p > 1) { throw new OutOfRangeException(p, 0, 1); } if (p == 0) { return a; } if (p == 1) { return b; } if (p < (c - a) / (b - a)) { return a + FastMath.sqrt(p * (b - a) * (c - a)); } return b - FastMath.sqrt((1 - p) * (b - a) * (b - c)); } }