/*
* 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>
*
* @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));
}
}