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Commons Math example source code file (GammaDistributionImpl.java)

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

Java - Commons Math tags/keywords

abstractcontinuousdistribution, default_inverse_absolute_accuracy, default_inverse_absolute_accuracy, deprecated, deprecated, gammadistribution, gammadistributionimpl, gammadistributionimpl, io, mathexception, override, override, serializable

The Commons Math GammaDistributionImpl.java 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.math.distribution;

import java.io.Serializable;

import org.apache.commons.math.MathException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.special.Gamma;

/**
 * The default implementation of {@link GammaDistribution}.
 *
 * @version $Revision: 925812 $ $Date: 2010-03-21 11:49:31 -0400 (Sun, 21 Mar 2010) $
 */
public class GammaDistributionImpl extends AbstractContinuousDistribution
    implements GammaDistribution, Serializable  {

    /**
     * Default inverse cumulative probability accuracy
     * @since 2.1
     */
    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;

    /** Serializable version identifier */
    private static final long serialVersionUID = -3239549463135430361L;

    /** The shape parameter. */
    private double alpha;

    /** The scale parameter. */
    private double beta;

    /** Inverse cumulative probability accuracy */
    private final double solverAbsoluteAccuracy;

    /**
     * Create a new gamma distribution with the given alpha and beta values.
     * @param alpha the shape parameter.
     * @param beta the scale parameter.
     */
    public GammaDistributionImpl(double alpha, double beta) {
        this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    }

    /**
     * Create a new gamma distribution with the given alpha and beta values.
     * @param alpha the shape parameter.
     * @param beta the scale parameter.
     * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
     * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
     * @since 2.1
     */
    public GammaDistributionImpl(double alpha, double beta, double inverseCumAccuracy) {
        super();
        setAlphaInternal(alpha);
        setBetaInternal(beta);
        solverAbsoluteAccuracy = inverseCumAccuracy;
    }

    /**
     * For this distribution, X, this method returns P(X < x).
     *
     * The implementation of this method is based on:
     * <ul>
     * <li>
     * <a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html">
     * Chi-Squared Distribution</a>, equation (9).
     * <li>Casella, G., & Berger, R. (1990). Statistical Inference.
     * Belmont, CA: Duxbury Press.</li>
     * </ul>
     *
     * @param x the value at which the CDF is evaluated.
     * @return CDF for this distribution.
     * @throws MathException if the cumulative probability can not be
     *            computed due to convergence or other numerical errors.
     */
    public double cumulativeProbability(double x) throws MathException{
        double ret;

        if (x <= 0.0) {
            ret = 0.0;
        } else {
            ret = Gamma.regularizedGammaP(alpha, x / beta);
        }

        return ret;
    }

    /**
     * For this distribution, X, this method returns the critical point x, such
     * that P(X < x) = <code>p.
     * <p>
     * Returns 0 for p=0 and <code>Double.POSITIVE_INFINITY for p=1.

* * @param p the desired probability * @return x, such that P(X < x) = <code>p * @throws MathException if the inverse cumulative probability can not be * computed due to convergence or other numerical errors. * @throws IllegalArgumentException if <code>p is not a valid * probability. */ @Override public double inverseCumulativeProbability(final double p) throws MathException { if (p == 0) { return 0d; } if (p == 1) { return Double.POSITIVE_INFINITY; } return super.inverseCumulativeProbability(p); } /** * Modify the shape parameter, alpha. * @param alpha the new shape parameter. * @throws IllegalArgumentException if <code>alpha is not positive. * @deprecated as of 2.1 (class will become immutable in 3.0) */ @Deprecated public void setAlpha(double alpha) { setAlphaInternal(alpha); } /** * Modify the shape parameter, alpha. * @param newAlpha the new shape parameter. * @throws IllegalArgumentException if <code>newAlpha is not positive. */ private void setAlphaInternal(double newAlpha) { if (newAlpha <= 0.0) { throw MathRuntimeException.createIllegalArgumentException( "alpha must be positive ({0})", newAlpha); } this.alpha = newAlpha; } /** * Access the shape parameter, alpha * @return alpha. */ public double getAlpha() { return alpha; } /** * Modify the scale parameter, beta. * @param newBeta the new scale parameter. * @throws IllegalArgumentException if <code>newBeta is not positive. * @deprecated as of 2.1 (class will become immutable in 3.0) */ @Deprecated public void setBeta(double newBeta) { setBetaInternal(newBeta); } /** * Modify the scale parameter, beta. * @param newBeta the new scale parameter. * @throws IllegalArgumentException if <code>newBeta is not positive. */ private void setBetaInternal(double newBeta) { if (newBeta <= 0.0) { throw MathRuntimeException.createIllegalArgumentException( "beta must be positive ({0})", newBeta); } this.beta = newBeta; } /** * Access the scale parameter, beta * @return beta. */ public double getBeta() { return beta; } /** * Returns the probability density for a particular point. * * @param x The point at which the density should be computed. * @return The pdf at point x. */ @Override public double density(double x) { if (x < 0) return 0; return Math.pow(x / beta, alpha - 1) / beta * Math.exp(-x / beta) / Math.exp(Gamma.logGamma(alpha)); } /** * Return the probability density for a particular point. * * @param x The point at which the density should be computed. * @return The pdf at point x. * @deprecated */ public double density(Double x) { return density(x.doubleValue()); } /** * Access the domain value lower bound, based on <code>p, used to * bracket a CDF root. This method is used by * {@link #inverseCumulativeProbability(double)} to find critical values. * * @param p the desired probability for the critical value * @return domain value lower bound, i.e. * P(X < <i>lower bound) < p */ @Override protected double getDomainLowerBound(double p) { // TODO: try to improve on this estimate return Double.MIN_VALUE; } /** * Access the domain value upper bound, based on <code>p, used to * bracket a CDF root. This method is used by * {@link #inverseCumulativeProbability(double)} to find critical values. * * @param p the desired probability for the critical value * @return domain value upper bound, i.e. * P(X < <i>upper bound) > p */ @Override protected double getDomainUpperBound(double p) { // TODO: try to improve on this estimate // NOTE: gamma is skewed to the left // NOTE: therefore, P(X < μ) > .5 double ret; if (p < .5) { // use mean ret = alpha * beta; } else { // use max value ret = Double.MAX_VALUE; } return ret; } /** * Access the initial domain value, based on <code>p, used to * bracket a CDF root. This method is used by * {@link #inverseCumulativeProbability(double)} to find critical values. * * @param p the desired probability for the critical value * @return initial domain value */ @Override protected double getInitialDomain(double p) { // TODO: try to improve on this estimate // Gamma is skewed to the left, therefore, P(X < μ) > .5 double ret; if (p < .5) { // use 1/2 mean ret = alpha * beta * .5; } else { // use mean ret = alpha * beta; } return ret; } /** * Return the absolute accuracy setting of the solver used to estimate * inverse cumulative probabilities. * * @return the solver absolute accuracy * @since 2.1 */ @Override protected double getSolverAbsoluteAccuracy() { return solverAbsoluteAccuracy; } }

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