ParetoDist.java

/*
 * Class:        ParetoDist
 * Description:  Pareto 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 ParetoDist extends ContinuousDistribution {
   private double alpha;
   private double beta;

   public ParetoDist(double alpha) {
      setParams(alpha, 1.0);
   }

   public ParetoDist(double alpha, double beta) {
      setParams(alpha, beta);
   }
 
   public double density(double x) {
      return density(alpha, beta, x);
   }
 
   public double cdf(double x) {
      return cdf(alpha, beta, x);
   }
 
   public double barF(double x) {
      return barF(alpha, beta, x);
   }
 
   public double inverseF(double u) {
      return inverseF(alpha, beta, u);
   }
 
   public double getMean() {
      return ParetoDist.getMean(alpha, beta);
   }
 
   public double getVariance() {
      return ParetoDist.getVariance(alpha, beta);
   }
 
   public double getStandardDeviation() {
      return ParetoDist.getStandardDeviation(alpha, beta);
   }

   public static double density(double alpha, double beta, double x) {
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 0");
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
 
      return x < beta ? 0 : alpha * Math.pow(beta / x, alpha) / x;
   }

   public static double cdf(double alpha, double beta, double x) {
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 0");
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (x <= beta)
         return 0.0;
      return 1.0 - Math.pow(beta / x, alpha);
   }

   public static double barF(double alpha, double beta, double x) {
      if (alpha <= 0)
         throw new IllegalArgumentException("c <= 0");
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (x <= beta)
         return 1.0;
      return Math.pow(beta / x, alpha);
   }

   public static double inverseF(double alpha, double beta, double u) {
      if (alpha <= 0)
         throw new IllegalArgumentException("c <= 0");
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
 
      if (u < 0.0 || u > 1.0)
         throw new IllegalArgumentException("u not in [0,1]");
 
      if (u <= 0.0)
         return beta;
 
      double t;
      t = -Math.log1p(-u);
      if ((u >= 1.0) || t / Math.log(10) >= alpha * Num.DBL_MAX_10_EXP)
         return Double.POSITIVE_INFINITY;
 
      return beta / Math.pow(1 - u, 1.0 / alpha);
   }

   public static double[] getMLE(double[] x, int n) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
 
      double[] parameters = new double[2];
      parameters[1] = Double.POSITIVE_INFINITY;
      for (int i = 0; i < n; i++) {
         if (x[i] < parameters[1])
            parameters[1] = x[i];
      }
 
      double sum = 0.0;
      for (int i = 0; i < n; i++) {
         if (x[i] > 0.0)
            sum += Math.log(x[i] / parameters[1]);
         else
            sum -= 709.0;
      }
      parameters[0] = n / sum;
      return parameters;
   }

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

   public static double getMean(double alpha, double beta) {
      if (alpha <= 1.0)
         throw new IllegalArgumentException("alpha <= 1");
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
 
      return ((alpha * beta) / (alpha - 1.0));
   }

   public static double getVariance(double alpha, double beta) {
      if (alpha <= 2)
         throw new IllegalArgumentException("alpha <= 2");
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
 
      return ((alpha * beta * beta) / ((alpha - 2.0) * (alpha - 1.0) * (alpha - 1.0)));
   }

   public static double getStandardDeviation(double alpha, double beta) {
      return Math.sqrt(ParetoDist.getVariance(alpha, beta));
   }

   public double getAlpha() {
      return alpha;
   }

   public double getBeta() {
      return beta;
   }

   public void setParams(double alpha, double beta) {
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 0");
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
 
      this.alpha = alpha;
      this.beta = beta;
      supportA = beta;
   }

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

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