LogisticDist.java

/*
 * Class:        LogisticDist
 * Description:  logistic 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 optimization.*;

public class LogisticDist extends ContinuousDistribution {
   private double alpha;
   private double lambda;
 
   private static class Optim implements Lmder_fcn {
      protected double[] xi;
      protected int n;
 
      public Optim(double[] x, int n) {
         this.n = n;
         this.xi = new double[n];
         System.arraycopy(x, 0, this.xi, 0, n);
      }
 
      public void fcn(int m, int n, double[] x, double[] fvec, double[][] fjac, int iflag[]) {
         if (x[2] <= 0.0) {
            final double BIG = 1.0e100;
            fvec[1] = BIG;
            fvec[2] = BIG;
            fjac[1][1] = BIG;
            fjac[1][2] = 0.0;
            fjac[2][1] = 0.0;
            fjac[2][2] = BIG;
            return;
         }
 
         double sum;
         double prod;
 
         if (iflag[1] == 1) {
            sum = 0.0;
            for (int i = 0; i < n; i++)
               sum += (1.0 / (1.0 + Math.exp(x[2] * (xi[i] - x[1]))));
            fvec[1] = sum - n / 2.0;
 
            sum = 0.0;
            for (int i = 0; i < n; i++) {
               prod = x[2] * (xi[i] - x[1]);
               sum -= prod * Math.tanh(prod / 2.0);
            }
            fvec[2] = sum - n;
         } else if (iflag[1] == 2) {
            sum = 0.0;
            for (int i = 0; i < n; i++) {
               prod = Math.exp(x[2] * (xi[i] - x[1]));
               sum -= x[2] * prod / ((1 + prod) * (1 + prod));
            }
            fjac[1][1] = sum;
 
            sum = 0.0;
            for (int i = 0; i < n; i++) {
               prod = Math.exp(x[2] * (xi[i] - x[1]));
               sum -= (xi[i] - x[1]) * prod / ((1 + prod) * (1 + prod));
            }
            fjac[1][2] = sum;
 
            sum = 0.0;
            for (int i = 0; i < n; i++) {
               prod = Math.exp(x[2] * (xi[i] - x[1]));
               sum -= (x[2] * ((-1.0 + prod) * (1.0 + prod) - (2.0 * (x[2] * (xi[i] - x[1])) * prod)))
                     / ((1.0 + prod) * (1.0 + prod));
            }
            fjac[2][1] = sum;
 
            sum = 0.0;
            for (int i = 0; i < n; i++) {
               prod = Math.exp(x[2] * (xi[i] - x[1]));
               sum -= ((x[1] - xi[1]) * ((-1.0 + prod) * (1.0 + prod) - (2.0 * (x[2] * (xi[i] - x[1])) * prod)))
                     / ((1.0 + prod) * (1.0 + prod));
            }
            fjac[2][2] = sum;
         }
      }
   }

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

   public LogisticDist(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 LogisticDist.getMean(alpha, lambda);
   }
 
   public double getVariance() {
      return LogisticDist.getVariance(alpha, lambda);
   }
 
   public double getStandardDeviation() {
      return LogisticDist.getStandardDeviation(alpha, lambda);
   }

   public static double density(double alpha, double lambda, double x) {
      if (lambda <= 0)
         throw new IllegalArgumentException("lambda <= 0");
      double z = lambda * (x - alpha);
      if (z >= -100.0) {
         double v = Math.exp(-z);
         return lambda * v / ((1.0 + v) * (1.0 + v));
      }
      return lambda * Math.exp(z);
   }

   public static double cdf(double alpha, double lambda, double x) {
      if (lambda <= 0)
         throw new IllegalArgumentException("lambda <= 0");
      double z = lambda * (x - alpha);
      if (z >= -100.0)
         return 1.0 / (1.0 + Math.exp(-z));
      return Math.exp(z);
   }

   public static double barF(double alpha, double lambda, double x) {
      if (lambda <= 0)
         throw new IllegalArgumentException("lambda <= 0");
      double z = lambda * (x - alpha);
      if (z <= 100.0)
         return 1.0 / (1.0 + Math.exp(z));
      return Math.exp(-z);
   }

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

   public static double[] getMLE(double[] x, int n) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
 
      double sum = 0.0;
      for (int i = 0; i < n; i++)
         sum += x[i];
 
      double[] param = new double[3];
      param[1] = sum / (double) n;
 
      sum = 0.0;
      for (int i = 0; i < n; i++)
         sum += ((x[i] - param[1]) * (x[i] - param[1]));
 
      param[2] = Math.sqrt(Math.PI * Math.PI * n / (3.0 * sum));
 
      double[] fvec = new double[3];
      double[][] fjac = new double[3][3];
      int[] iflag = new int[2];
      int[] info = new int[2];
      int[] ipvt = new int[3];
      Optim system = new Optim(x, n);
 
      Minpack_f77.lmder1_f77(system, 2, 2, param, fvec, fjac, 1e-5, info, ipvt);
 
      double parameters[] = new double[2];
      parameters[0] = param[1];
      parameters[1] = param[2];
 
      return parameters;
   }

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

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

   public static double getVariance(double alpha, double lambda) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
 
      return ((Math.PI * Math.PI / 3) * (1 / (lambda * lambda)));
   }

   public static double getStandardDeviation(double alpha, double lambda) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
 
      return (Math.sqrt(1.0 / 3.0) * 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;
   }
 
}