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Java example source code file (TriangularDistribution.java)

This example Java source code file (TriangularDistribution.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

abstractrealdistribution, numberistoolargeexception, numberistoosmallexception, outofrangeexception, override, triangulardistribution, well19937c

The TriangularDistribution.java Java example source code

/*
 * 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: 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>{@code 2 / (b - a)} if {@code x = c},
     * <li>{@code 2 * (b - x) / [(b - a) * (b - c)]} if {@code c < x <= b},
     * <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>{@code (x - a)^2 / [(b - a) * (c - a)]} if {@code a <= x < c},
     * <li>{@code (c - a) / (b - a)} if {@code x = c},
     * <li>{@code 1 - (b - x)^2 / [(b - a) * (b - c)]} if {@code c < x <= b},
     * <li>{@code 1} if {@code x > b}.
     * </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));
    }
}

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