LogarithmicDist.java

/*
 * Class:        LogarithmicDist
 * Description:  logarithmic 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;
import umontreal.ssj.util.RootFinder;
import umontreal.ssj.functions.MathFunction;

public class LogarithmicDist extends DiscreteDistributionInt {
 
   private double theta;
   private double t;
 
   private static class Function implements MathFunction {
      protected double mean;
 
      public Function(double mean) {
         this.mean = mean;
      }
 
      public double evaluate(double x) {
         if (x <= 0.0 || x >= 1.0)
            return 1.0e200;
         return (x + mean * (1.0 - x) * Math.log1p(-x));
      }
   }

   public LogarithmicDist(double theta) {
      setTheta(theta);
   }
 
   public double prob(int x) {
      if (x < 1)
         return 0;
      return t * Math.pow(theta, x) / x;
   }
 
   public double cdf(int x) {
      if (x < 1)
         return 0;
      double res = prob(1);
      double term = res;
      for (int i = 2; i <= x; i++) {
         term *= theta;
         res += term / i;
      }
      return res;
   }
 
   public double barF(int x) {
      if (x <= 1)
         return 1.0;
      double res = prob(x);
      double term = res;
      int i = x + 1;
      while (term > EPSILON) {
         term *= theta * (i - 1) / i;
         res += term;
      }
      return res;
   }
 
   public int inverseFInt(double u) {
      return inverseF(theta, u);
   }
 
   public double getMean() {
      return LogarithmicDist.getMean(theta);
   }
 
   public double getVariance() {
      return LogarithmicDist.getVariance(theta);
   }
 
   public double getStandardDeviation() {
      return LogarithmicDist.getStandardDeviation(theta);
   }

   public static double prob(double theta, int x) {
      if (theta <= 0 || theta >= 1)
         throw new IllegalArgumentException("theta not in range (0,1)");
      if (x < 1)
         return 0;
      return -1.0 / Math.log1p(-theta) * Math.pow(theta, x) / x;
   }

   public static double cdf(double theta, int x) {
      if (theta <= 0 || theta >= 1)
         throw new IllegalArgumentException("theta not in range (0,1)");
      if (x < 1)
         return 0;
      double res = prob(theta, 1);
      double term = res;
      for (int i = 2; i <= x; i++) {
         term *= theta;
         res += term / i;
      }
      return res;
   }

   public static double barF(double theta, int x) {
      if (theta <= 0 || theta >= 1)
         throw new IllegalArgumentException("theta not in range (0,1)");
      if (x <= 1)
         return 1.0;
      double res = prob(theta, x);
      double term = res;
      int i = x + 1;
      while (term > EPSILON) {
         term *= theta * (i - 1) / i;
         res += term;
      }
      return res;
   }
 
   public static int inverseF(double theta, double u) {
      throw new UnsupportedOperationException();
   }

   public static double[] getMLE(int[] x, int n) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
 
      double parameters[];
      parameters = new double[1];
      double sum = 0.0;
      for (int i = 0; i < n; i++) {
         sum += x[i];
      }
 
      double mean = (double) sum / (double) n;
 
      Function f = new Function(mean);
      parameters[0] = RootFinder.brentDekker(1e-15, 1.0 - 1e-15, f, 1e-7);
 
      return parameters;
   }

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

   public static double getMean(double theta) {
      if (theta <= 0.0 || theta >= 1.0)
         throw new IllegalArgumentException("theta not in range (0,1)");
 
      return ((-1 / Math.log1p(-theta)) * (theta / (1 - theta)));
   }

   public static double getVariance(double theta) {
      if (theta <= 0.0 || theta >= 1.0)
         throw new IllegalArgumentException("theta not in range (0,1)");
 
      double v = Math.log1p(-theta);
      return ((-theta * (theta + v)) / ((1 - theta) * (1 - theta) * v * v));
   }

   public static double getStandardDeviation(double theta) {
      return Math.sqrt(LogarithmicDist.getVariance(theta));
   }

   public double getTheta() {
      return theta;
   }

   public void setTheta(double theta) {
      if (theta <= 0 || theta >= 1)
         throw new IllegalArgumentException("theta not in range (0,1)");
      this.theta = theta;
      t = -1.0 / Math.log1p(-theta);
      supportA = 1;
   }

   public double[] getParams() {
      double[] retour = { theta };
      return retour;
   }

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