| /* |
| * 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.statistics.distribution; |
| |
| /** |
| * Implementation of the triangular real distribution. |
| * |
| * @see <a href="http://en.wikipedia.org/wiki/Triangular_distribution"> |
| * Triangular distribution (Wikipedia)</a> |
| */ |
| public class TriangularDistribution extends AbstractContinuousDistribution { |
| /** 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; |
| |
| /** |
| * Creates a distribution. |
| * |
| * @param a Lower limit of this distribution (inclusive). |
| * @param c Mode of this distribution. |
| * @param b Upper limit of this distribution (inclusive). |
| * @throws IllegalArgumentException if {@code a >= b}, if {@code c > b} |
| * or if {@code c < a}. |
| */ |
| public TriangularDistribution(double a, |
| double c, |
| double b) { |
| if (a >= b) { |
| throw new DistributionException(DistributionException.INVALID_RANGE_LOW_GTE_HIGH, |
| a, b); |
| } |
| if (c < a) { |
| throw new DistributionException(DistributionException.TOO_SMALL, |
| c, a); |
| } |
| if (c > b) { |
| throw new DistributionException(DistributionException.TOO_LARGE, |
| c, b); |
| } |
| |
| this.a = a; |
| this.c = c; |
| this.b = b; |
| } |
| |
| /** |
| * Gets the mode. |
| * |
| * @return the mode of the distribution. |
| */ |
| public double getMode() { |
| return c; |
| } |
| |
| /** |
| * {@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> |
| */ |
| @Override |
| public double density(double x) { |
| if (x < a) { |
| return 0; |
| } |
| if (x < c) { |
| final double divident = 2 * (x - a); |
| final double divisor = (b - a) * (c - a); |
| return divident / divisor; |
| } |
| if (x == c) { |
| return 2 / (b - a); |
| } |
| if (x <= b) { |
| final double divident = 2 * (b - x); |
| final 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> |
| */ |
| @Override |
| public double cumulativeProbability(double x) { |
| if (x < a) { |
| return 0; |
| } |
| if (x < c) { |
| final double divident = (x - a) * (x - a); |
| final double divisor = (b - a) * (c - a); |
| return divident / divisor; |
| } |
| if (x == c) { |
| return (c - a) / (b - a); |
| } |
| if (x <= b) { |
| final double divident = (b - x) * (b - x); |
| final 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}. |
| */ |
| @Override |
| public double getMean() { |
| 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}. |
| */ |
| @Override |
| public double getVariance() { |
| 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 |
| */ |
| @Override |
| 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 |
| */ |
| @Override |
| public double getSupportUpperBound() { |
| return b; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * |
| * The support of this distribution is connected. |
| * |
| * @return {@code true} |
| */ |
| @Override |
| public boolean isSupportConnected() { |
| return true; |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public double inverseCumulativeProbability(double p) { |
| if (p < 0 || |
| p > 1) { |
| throw new DistributionException(DistributionException.INVALID_PROBABILITY, p); |
| } |
| if (p == 0) { |
| return a; |
| } |
| if (p == 1) { |
| return b; |
| } |
| if (p < (c - a) / (b - a)) { |
| return a + Math.sqrt(p * (b - a) * (c - a)); |
| } |
| return b - Math.sqrt((1 - p) * (b - a) * (b - c)); |
| } |
| } |