ExponentialDistribution.java

/*
 * ExponentialDistribution.java
 *
 * Copyright (c) 2002-2015 Alexei Drummond, Andrew Rambaut and Marc Suchard
 *
 * This file is part of BEAST.
 * See the NOTICE file distributed with this work for additional
 * information regarding copyright ownership and licensing.
 *
 * BEAST is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as
 * published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 *  BEAST is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with BEAST; if not, write to the
 * Free Software Foundation, Inc., 51 Franklin St, Fifth Floor,
 * Boston, MA  02110-1301  USA
 */

package dr.math.distributions;

import dr.math.UnivariateFunction;

/**
 * exponential distribution.
 * <p/>
 * (Parameter: lambda; mean: 1/lambda; variance: 1/lambda^2)
 * <p/>
 * The exponential distribution is a special case of the Gamma distribution
 * (shape parameter = 1.0, scale = 1/lambda).
 *
 * @author Alexei Drummond
 * @author Korbinian Strimmer
 * @version $Id: ExponentialDistribution.java,v 1.5 2005/05/24 20:26:00 rambaut Exp $
 */
public class ExponentialDistribution implements Distribution {
    //
    // Public stuff
    //

    /**
     * Constructor
     *
     * @param lambda the rate of the exponential distribution (1/mean)
     */
    public ExponentialDistribution(double lambda) {
        this.lambda = lambda;
    }

    public double pdf(double x) {
        return pdf(x, lambda);
    }

    public double logPdf(double x) {
        return logPdf(x, lambda);
    }

    public double cdf(double x) {
        return cdf(x, lambda);
    }

    public double quantile(double y) {
        return quantile(y, lambda);
    }

    public double mean() {
        return mean(lambda);
    }

    public double variance() {
        return variance(lambda);
    }

    public UnivariateFunction getProbabilityDensityFunction() {
        return pdfFunction;
    }

    private UnivariateFunction pdfFunction = new UnivariateFunction() {
        public final double evaluate(double x) {
            return pdf(x);
        }

        public final double getLowerBound() {
            return 0.0;
        }

        public final double getUpperBound() {
            return Double.POSITIVE_INFINITY;
        }
    };

    /**
     * probability density function of the exponential distribution
     * (mean = 1/lambda)
     *
     * @param x      argument
     * @param lambda parameter of exponential distribution
     * @return pdf value
     */
    public static double pdf(double x, double lambda) {
    	if (x < 0) return 0;
    	
        return lambda * Math.exp(-lambda * x);
    }

    /**
     * the natural log of the probability density function of the distribution
     * (mean = 1/lambda)
     *
     * @param x      argument
     * @param lambda parameter of exponential distribution
     * @return log pdf value
     */
    public static double logPdf(double x, double lambda) {
    	if (x < 0) return Double.NEGATIVE_INFINITY;
    	
        return Math.log(lambda) - (lambda * x);
    }

    /**
     * cumulative density function of the exponential distribution
     *
     * @param x      argument
     * @param lambda parameter of exponential distribution
     * @return cdf value
     */
    public static double cdf(double x, double lambda) {
        return 1.0 - Math.exp(-lambda * x);
    }


    /**
     * quantile (inverse cumulative density function) of the exponential distribution
     *
     * @param y      argument
     * @param lambda parameter of exponential distribution
     * @return icdf value
     */
    public static double quantile(double y, double lambda) {
        return -(1.0 / lambda) * Math.log(1.0 - y);
    }

    /**
     * mean of the exponential distribution
     *
     * @param lambda parameter of exponential distribution
     * @return mean
     */
    public static double mean(double lambda) {
        return 1.0 / (lambda);
    }

    /**
     * variance of the exponential distribution
     *
     * @param lambda parameter of exponential distribution
     * @return variance
     */
    public static double variance(double lambda) {
        return 1.0 / (lambda * lambda);
    }

    // the rate parameter of this exponential distribution (1/mean)
    double lambda;
}