ExtremeValueDist.java

/*
 * Class:        ExtremeValueDist
 * 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;

@Deprecated
public class ExtremeValueDist extends ContinuousDistribution {
   private double alpha;
   private double lambda;
 
   private static class Function implements MathFunction {
      protected int n;
      protected double mean;
      protected double[] x;
 
      public Function(double[] x, int n, double mean) {
         this.n = n;
         this.mean = mean;
         this.x = new double[n];
 
         System.arraycopy(x, 0, this.x, 0, n);
      }
 
      public double evaluate(double lambda) {
         if (lambda <= 0.0)
            return 1.0e200;
         double exp = 0.0;
         double sumXiExp = 0.0;
         double sumExp = 0.0;
 
         for (int i = 0; i < n; i++) {
            exp = Math.exp(-x[i] * lambda);
            sumExp += exp;
            sumXiExp += x[i] * exp;
         }
 
         return ((mean - 1.0 / lambda) * sumExp - sumXiExp);
      }
   }

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

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

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

   public static double cdf(double alpha, double lambda, double x) {
      if (lambda <= 0)
         throw new IllegalArgumentException("lambda <= 0");
      final double z = lambda * (x - alpha);
      if (z <= -10.0)
         return 0.0;
      if (z >= XBIG)
         return 1.0;
      return Math.exp(-Math.exp(-z));
   }

   public static double barF(double alpha, double lambda, double x) {
      if (lambda <= 0)
         throw new IllegalArgumentException("lambda <= 0");
      final double z = lambda * (x - alpha);
      if (z <= -10.0)
         return 1.0;
      if (z >= XBIGM)
         return 0.0;
      return -Math.expm1(-Math.exp(-z));
   }

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

   public static double[] getMLE(double[] x, int n) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
 
      double parameters[] = new double[2];
 
      double sum = 0.0;
      for (int i = 0; i < n; i++)
         sum += x[i];
      double mean = sum / (double) n;
 
      sum = 0.0;
      for (int i = 0; i < n; i++)
         sum += (x[i] - mean) * (x[i] - mean);
      double variance = sum / ((double) n - 1.0);
 
      double lambda0 = Math.PI / Math.sqrt(6 * variance);
 
      Function f = new Function(x, n, mean);
 
      double a;
      if ((a = lambda0 - 10.0) < 0)
         a = 1e-15;
      parameters[1] = RootFinder.brentDekker(a, lambda0 + 10.0, f, 1e-7);
 
      double sumExp = 0.0;
      for (int i = 0; i < n; i++)
         sumExp += Math.exp(-x[i] * parameters[1]);
      parameters[0] = -Math.log(sumExp / (double) n) / parameters[1];
 
      return parameters;
   }

   @Deprecated
   public static double[] getMaximumLikelihoodEstimate(double[] x, int n) {
      return getMLE(x, n);
   }

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

   public static double getMean(double alpha, double lambda) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
 
      return (alpha + Num.EULER / lambda);
   }

   public static double getVariance(double alpha, double lambda) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
 
      return ((1.0 / 6.0 * Math.PI * Math.PI) * (1.0 / (lambda * lambda)));
   }

   public static double getStandardDeviation(double alpha, double lambda) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
 
      return (Math.sqrt(1.0 / 6.0) * Math.PI / lambda);
   }

   public double getAlpha() {
      return alpha;
   }

   public double getLambda() {
      return lambda;
   }

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

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

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