LaplaceDist.java

/*
 * Class:        LaplaceDist
 * Description:  Laplace distribution
 * Environment:  Java
 * Software:     SSJ 
 * Copyright (C) 2001  Pierre L'Ecuyer and Universite de Montreal
 * Organization: DIRO, Universite de Montreal
 * @author       
 * @since
 *
 *
 * Licensed 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 umontreal.ssj.probdist;
 
import umontreal.ssj.util.Num;

public class LaplaceDist extends ContinuousDistribution {
   private double mu;
   private double beta;

   public LaplaceDist() {
      mu = 0;
      beta = 1;
   }

   public LaplaceDist(double mu, double beta) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
 
      this.mu = mu;
      this.beta = beta;
   }
 
   public double density(double x) {
      return density(mu, beta, x);
   }
 
   public double cdf(double x) {
      return cdf(mu, beta, x);
   }
 
   public double barF(double x) {
      return barF(mu, beta, x);
   }
 
   public double inverseF(double u) {
      return inverseF(mu, beta, u);
   }
 
   public double getMean() {
      return LaplaceDist.getMean(mu, beta);
   }
 
   public double getVariance() {
      return LaplaceDist.getVariance(mu, beta);
   }
 
   public double getStandardDeviation() {
      return LaplaceDist.getStandardDeviation(mu, beta);
   }

   public static double density(double mu, double beta, double x) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      return Math.exp(-Math.abs(x - mu) / beta) / (2.0 * beta);
   }

   public static double cdf(double mu, double beta, double x) {
      if (x <= mu)
         return Math.exp((x - mu) / beta) / 2.0;
      else
         return 1.0 - Math.exp((mu - x) / beta) / 2.0;
   }

   public static double barF(double mu, double beta, double x) {
      if (x <= mu)
         return 1.0 - Math.exp((x - mu) / beta) / 2.0;
      else
         return Math.exp((mu - x) / beta) / 2.0;
   }
 
   // ====================================================
   // code taken and adapted from unuran
   // file /distribution/c_laplca_gen.c
   // ====================================================

   public static double inverseF(double mu, double beta, double u) {
      // transform to random variate
      if (u < 0.0 || u > 1.0)
         throw new IllegalArgumentException("u should be in [0,1]");
      if (u <= 0.0)
         return Double.NEGATIVE_INFINITY;
      if (u >= 1.0)
         return Double.POSITIVE_INFINITY;
 
      double x = (u > 0.5) ? -Math.log(2. - 2 * u) : Math.log(2 * u);
      return mu + beta * x;
   }

   public static double[] getMLE(double[] x, int n) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
 
      double parameters[];
      parameters = new double[2];
 
      parameters[0] = EmpiricalDist.getMedian(x, n);
 
      double sum = 0.0;
      for (int i = 0; i < n; i++)
         sum += Math.abs(x[i] - parameters[0]);
      parameters[1] = sum / (double) n;
 
      return parameters;
   }

   public static LaplaceDist getInstanceFromMLE(double[] x, int n) {
      double parameters[] = getMLE(x, n);
      return new LaplaceDist(parameters[0], parameters[1]);
   }

   public static double getMean(double mu, double beta) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
 
      return mu;
   }

   public static double getVariance(double mu, double beta) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
 
      return (2.0 * beta * beta);
   }

   public static double getStandardDeviation(double mu, double beta) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
 
      return (Num.RAC2 * beta);
   }

   public double getMu() {
      return mu;
   }

   public double getBeta() {
      return beta;
   }

   public double[] getParams() {
      double[] retour = { mu, beta };
      return retour;
   }

   public String toString() {
      return getClass().getSimpleName() + " : mu = " + mu + ", beta = " + beta;
   }
 
}