GumbelDist.java

/*
 * Class:        GumbelDist
 * Description:  Gumbel 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 GumbelDist extends ContinuousDistribution {
   private double delta;
   private double beta;
 
   private static class FunctionPlus implements MathFunction {
      // when beta > 0
      protected int n;
      protected double mean;
      protected double[] x;
      private double minx; // min of all {x[i]}
 
      public FunctionPlus(double[] y, int n, double mean, double minx) {
         this.n = n;
         this.mean = mean;
         this.x = y;
         this.minx = minx;
      }
 
      public double evaluate(double lam) {
         if (lam <= 0.0)
            return 1.0e100;
         double tem;
         double sum2 = 0.0;
         double sum1 = 0.0;
 
         for (int i = 0; i < n; i++) {
            tem = Math.exp(-(x[i] - minx) * lam);
            sum1 += tem;
            sum2 += x[i] * tem;
         }
 
         return (mean - 1 / lam) * sum1 - sum2;
      }
   }
 
   private static class FunctionMinus implements MathFunction {
      // when beta < 0
      protected int n;
      protected double mean;
      protected double[] x;
      protected double xmax;
 
      public FunctionMinus(double[] y, int n, double mean, double xmax) {
         this.n = n;
         this.mean = mean;
         this.x = y;
         this.xmax = xmax;
      }
 
      public double evaluate(double lam) {
         if (lam >= 0.0)
            return 1.0e100;
         double tem;
         double sum2 = 0.0;
         double sum1 = 0.0;
 
         for (int i = 0; i < n; i++) {
            tem = Math.exp((xmax - x[i]) * lam);
            sum1 += tem;
            sum2 += x[i] * tem;
         }
 
         return (mean - 1 / lam) * sum1 - sum2;
      }
   }

   public GumbelDist() {
      setParams(1.0, 0.0);
   }

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

   public static double density(double beta, double delta, double x) {
      if (beta == 0.)
         throw new IllegalArgumentException("beta = 0");
      final double z = (x - delta) / beta;
      if (z <= -10.0)
         return 0.0;
      double t = Math.exp(-z);
      return t * Math.exp(-t) / Math.abs(beta);
   }

   public static double cdf(double beta, double delta, double x) {
      if (beta == 0.)
         throw new IllegalArgumentException("beta = 0");
      final double z = (x - delta) / beta;
      if (beta > 0.) {
         if (z <= -7.0)
            return 0.0;
         return Math.exp(-Math.exp(-z));
      } else { // beta < 0
         if (z <= -7.0)
            return 1.0;
         return -Math.expm1(-Math.exp(-z));
      }
   }

   public static double barF(double beta, double delta, double x) {
      if (beta == 0.)
         throw new IllegalArgumentException("beta = 0");
      final double z = (x - delta) / beta;
      if (beta > 0.) {
         if (z <= -7.0)
            return 1.0;
         return -Math.expm1(-Math.exp(-z));
      } else { // beta < 0
         if (z <= -7.0)
            return 0.0;
         return Math.exp(-Math.exp(-z));
      }
   }

   public static double inverseF(double beta, double delta, double u) {
      if (u < 0.0 || u > 1.0)
         throw new IllegalArgumentException("u not in [0, 1]");
      if (beta == 0.)
         throw new IllegalArgumentException("beta = 0");
      if (u >= 1.0)
         return Double.POSITIVE_INFINITY;
      if (u <= 0.0)
         return Double.NEGATIVE_INFINITY;
      if (beta > 0.)
         return delta - Math.log(-Math.log(u)) * beta;
      else
         return delta - Math.log(-Math.log1p(-u)) * beta;
   }

   public static double[] getMLE(double[] x, int n) {
      if (n <= 1)
         throw new IllegalArgumentException("n <= 1");
      int i;
      double par[] = new double[2];
 
      double xmin = Double.MAX_VALUE;
      double sum = 0;
      for (i = 0; i < n; i++) {
         sum += x[i];
         if (x[i] < xmin)
            xmin = x[i];
      }
      double mean = sum / (double) n;
 
      sum = 0;
      for (i = 0; i < n; i++)
         sum += (x[i] - mean) * (x[i] - mean);
      double variance = sum / (n - 1.0);
 
      FunctionPlus func = new FunctionPlus(x, n, mean, xmin);
 
      double lam = 1.0 / (0.7797 * Math.sqrt(variance));
      final double EPS = 0.02;
      double a = (1.0 - EPS) * lam - 5.0;
      if (a <= 0)
         a = 1e-15;
      double b = (1.0 + EPS) * lam + 5.0;
      lam = RootFinder.brentDekker(a, b, func, 1e-8);
      par[0] = 1.0 / lam;
 
      sum = 0;
      for (i = 0; i < n; i++)
         sum += Math.exp(-(x[i] - xmin) * lam);
      par[1] = xmin - Math.log(sum / n) / lam;
      return par;
   }

   public static double[] getMLEmin(double[] x, int n) {
      if (n <= 1)
         throw new IllegalArgumentException("n <= 1");
 
      int i;
      double par[] = new double[2];
      double xmax = -Double.MAX_VALUE;
      double sum = 0.0;
      for (i = 0; i < n; i++) {
         sum += x[i];
         if (x[i] > xmax)
            xmax = x[i];
      }
      double mean = sum / (double) n;
 
      sum = 0.0;
      for (i = 0; i < n; i++)
         sum += (x[i] - mean) * (x[i] - mean);
      double variance = sum / (n - 1.0);
 
      FunctionMinus func = new FunctionMinus(x, n, mean, xmax);
 
      double lam = -1.0 / (0.7797 * Math.sqrt(variance));
      final double EPS = 0.02;
      double a = (1.0 + EPS) * lam - 2.0;
      double b = (1.0 - EPS) * lam + 2.0;
      if (b >= 0)
         b = -1e-15;
      lam = RootFinder.brentDekker(a, b, func, 1e-12);
      par[0] = 1.0 / lam;
 
      sum = 0.0;
      for (i = 0; i < n; i++)
         sum += Math.exp((xmax - x[i]) * lam);
      par[0] = 1.0 / lam;
      par[1] = xmax - Math.log(sum / n) / lam;
 
      return par;
   }

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

   public static GumbelDist getInstanceFromMLEmin(double[] x, int n) {
      double parameters[] = getMLEmin(x, n);
      return new GumbelDist(parameters[0], parameters[1]);
   }

   public static double getMean(double beta, double delta) {
      if (beta == 0.0)
         throw new IllegalArgumentException("beta = 0");
 
      return delta + Num.EULER * beta;
   }

   public static double getVariance(double beta, double delta) {
      if (beta == 0.0)
         throw new IllegalArgumentException("beta = 0");
 
      return Math.PI * Math.PI * beta * beta / 6.0;
   }

   public static double getStandardDeviation(double beta, double delta) {
      if (beta == 0.0)
         throw new IllegalArgumentException("beta = 0");
 
      return Math.sqrt(getVariance(beta, delta));
   }

   public double getBeta() {
      return beta;
   }

   public double getDelta() {
      return delta;
   }

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

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

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