LoglogisticDist.java

/*
 * Class:        LoglogisticDist
 * Description:  log-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 umontreal.ssj.util.Num;
import umontreal.ssj.util.Misc;
import optimization.*;

public class LoglogisticDist extends ContinuousDistribution {
   private double alpha;
   private double beta;
 
   private static class Optim implements Uncmin_methods {
      private int n;
      private double[] xi;
 
      public Optim(double[] x, int n) {
         this.n = n;
         this.xi = new double[n];
         System.arraycopy(x, 0, this.xi, 0, n);
      }
 
      public double f_to_minimize(double[] p) {
         if ((p[1] <= 0.0) || (p[2] <= 0.0))
            return 1e200;
 
         double sum = 0.0;
         for (int i = 0; i < n; i++) {
            double tmp = density(p[1], p[2], xi[i]);
            if (tmp > 0.0)
               sum -= Math.log(tmp);
            else
               sum += 709.0; // log (Double.MIN_VALUE)
         }
         return sum;
      }
 
      public void gradient(double[] x, double[] g) {
      }
 
      public void hessian(double[] x, double[][] h) {
      }
   }

   public LoglogisticDist(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 getMean(alpha, beta);
   }
 
   public double getVariance() {
      return getVariance(alpha, beta);
   }
 
   public double getStandardDeviation() {
      return getStandardDeviation(alpha, beta);
   }

   public static double density(double alpha, double beta, double x) {
      double denominateur;
 
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 0");
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (x <= 0.0 || x >= Double.MAX_VALUE / 2.0)
         return 0.0;
 
      if (x <= beta) {
         double v = Math.pow(x / beta, alpha);
         denominateur = 1.0 + v;
         denominateur *= denominateur * beta;
         return alpha * v * beta / (x * denominateur);
      } else {
         double v = Math.pow(beta / x, alpha);
         denominateur = 1.0 + v;
         denominateur *= denominateur * beta;
         return alpha * v * beta / (x * denominateur);
      }
   }

   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 <= 0.0)
         return 0.0;
      if (x >= Double.MAX_VALUE / 2.0)
         return 1.0;
      double z = x / beta;
      if (z >= 1.0)
         return 1.0 / (1.0 + Math.pow(1.0 / z, alpha));
      double v = Math.pow(z, alpha);
      return v / (v + 1.0);
   }

   public static double barF(double alpha, double beta, double x) {
      double power;
 
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 0");
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (x <= 0.0)
         return 1.0;
      if (x >= Double.MAX_VALUE / 2.0)
         return 0.0;
 
      double z = x / beta;
      if (z <= 1.0)
         return 1.0 / (1.0 + Math.pow(z, alpha));
      double v = Math.pow(1.0 / z, alpha);
      return v / (v + 1.0);
   }

   public static double inverseF(double alpha, double beta, double u) {
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 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 >= 1.0)
         return Double.POSITIVE_INFINITY;
      if (u <= 0.0)
         return 0.0;
 
      if (u <= 0.5)
         return (beta * Math.pow(u / (1.0 - u), 1.0 / alpha));
      else
         return (beta / Math.pow((1.0 - u) / u, 1.0 / alpha));
   }

   public static double[] getMLE(double[] x, int n) {
      double sum = 0.0;
 
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
 
      Optim system = new Optim(x, n);
 
      double[] parameters = new double[2];
      double[] xpls = new double[3];
      double[] param = new double[3];
      double[] fpls = new double[3];
      double[] gpls = new double[3];
      int[] itrcmd = new int[2];
      double[][] a = new double[3][3];
      double[] udiag = new double[3];
 
      param[2] = EmpiricalDist.getMedian(x, n);
 
      if (param[2] < 0)
         throw new IllegalArgumentException("median < 0");
      if (param[2] <= 0)
         param[2] = 1.0;
 
      int m = Math.round((float) n / 4.0f);
      double q1 = Misc.quickSelect(x, n, m);
 
      if (q1 < 0)
         throw new IllegalArgumentException("x[i] < 0");
      if (q1 > 0)
         param[1] = Math.log(3) / (Math.log(param[2]) - Math.log(q1));
      else
         param[1] = 1.0;
 
      Uncmin_f77.optif0_f77(2, param, system, xpls, fpls, gpls, itrcmd, a, udiag);
 
      for (int i = 0; i < 2; i++)
         parameters[i] = xpls[i + 1];
 
      return parameters;
   }

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

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

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

   public static double getStandardDeviation(double alpha, double beta) {
      return Math.sqrt(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 = 0.0;
   }

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

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