CauchyDist.java

/*
 * Class:        CauchyDist
 * Description:  Cauchy distribution
 * Environment:  Java
 * Software:     SSJ
 * Copyright (C) 2001  Pierre L'Ecuyer and Universite de Montreal
 * Organization: DIRO, Universite de Montreal
 * @author       Richard Simard
 * @since        March 2009
 *
 *
 * 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.Misc;
import optimization.*;

public class CauchyDist 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) {
         double sum = 0.0;
 
         if (p[2] <= 0.0) // barrier at 0
            return 1.0e200;
 
         for (int i = 0; i < n; i++)
            sum -= Math.log(density(p[1], p[2], xi[i]));
 
         return sum;
      }
 
      public void gradient(double[] x, double[] g) {
      }
 
      public void hessian(double[] x, double[][] h) {
      }
   }

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

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

   public static double density(double alpha, double beta, double x) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      double t = (x - alpha) / beta;
      return 1.0 / (beta * Math.PI * (1 + t * t));
   }

   public static double cdf(double alpha, double beta, double x) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      double z = (x - alpha) / beta;
      if (z < -0.5)
         return Math.atan(-1. / z) / Math.PI;
      return Math.atan(z) / Math.PI + 0.5;
   }

   public static double barF(double alpha, double beta, double x) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      double z = (x - alpha) / beta;
      if (z > 0.5)
         return Math.atan(1. / z) / Math.PI;
      return 0.5 - Math.atan(z) / Math.PI;
   }

   public static double inverseF(double alpha, double beta, double u) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (u < 0.0 || u > 1.0)
         throw new IllegalArgumentException("u must be in [0,1]");
      if (u <= 0.0)
         return Double.NEGATIVE_INFINITY;
      if (u >= 1.0)
         return Double.POSITIVE_INFINITY;
      if (u < 0.5)
         return alpha - 1.0 / Math.tan(Math.PI * u) * beta;
      return alpha + Math.tan(Math.PI * (u - 0.5)) * beta;
   }

   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[1] = EmpiricalDist.getMedian(x, n);
 
      int m = Math.round((float) n / 4.0f);
      double q3 = Misc.quickSelect(x, n, 3 * m);
      double q1 = Misc.quickSelect(x, n, m);
      param[2] = (q3 - q1) / 2.0;
 
      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 CauchyDist getInstanceFromMLE(double[] x, int n) {
      double parameters[] = getMLE(x, n);
      return new CauchyDist(parameters[0], parameters[1]);
   }

   public static double getMean(double alpha, double beta) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
 
      throw new UnsupportedOperationException("Undefined mean");
   }

   public static double getVariance(double alpha, double beta) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
 
      return Double.POSITIVE_INFINITY;
   }

   public static double getStandardDeviation(double alpha, double beta) {
      return Double.POSITIVE_INFINITY;
   }

   public double getAlpha() {
      return alpha;
   }

   public double getBeta() {
      return beta;
   }

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

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

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