| /* |
| * 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.random.RandomGenerator; |
| import org.apache.commons.math3.random.Well19937c; |
| import org.apache.commons.math3.util.FastMath; |
| |
| /** |
| * Implementation of the triangular real distribution. |
| * |
| * @see <a href="http://en.wikipedia.org/wiki/Triangular_distribution"> |
| * Triangular distribution (Wikipedia)</a> |
| * |
| * @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. |
| * <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 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; |
| } |
| |
| /** {@inheritDoc} */ |
| @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)); |
| } |
| } |
