HyperbolicSecantDist.java

/*
 * Class:        HyperbolicSecantDist
 * Description:  hyperbolic secant 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 HyperbolicSecantDist extends ContinuousDistribution {
   protected double mu;
   protected double sigma;
   private static final double ZLIMB = 500.0;
   private static final double ZLIMS = 50.0;
 
   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)
            return 1e200;
 
         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 HyperbolicSecantDist(double mu, double sigma) {
      setParams(mu, sigma);
   }
 
   public double density(double x) {
      return HyperbolicSecantDist.density(mu, sigma, x);
   }
 
   public double cdf(double x) {
      return HyperbolicSecantDist.cdf(mu, sigma, x);
   }
 
   public double barF(double x) {
      return HyperbolicSecantDist.barF(mu, sigma, x);
   }
 
   public double inverseF(double u) {
      return HyperbolicSecantDist.inverseF(mu, sigma, u);
   }
 
   public double getMean() {
      return HyperbolicSecantDist.getMean(mu, sigma);
   }
 
   public double getVariance() {
      return HyperbolicSecantDist.getVariance(mu, sigma);
   }
 
   public double getStandardDeviation() {
      return HyperbolicSecantDist.getStandardDeviation(mu, sigma);
   }

   public static double density(double mu, double sigma, double x) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      double y = (x - mu) / sigma;
      if (Math.abs(y) >= ZLIMB)
         return 0.0;
      else
         return (1.0 / (Math.cosh(Math.PI * y / 2.0) * 2.0 * sigma));
   }

   public static double cdf(double mu, double sigma, double x) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      double y = (x - mu) / sigma;
      if (y >= ZLIMS)
         return 1.0;
      else if (y <= -ZLIMB)
         return 0.0;
      else
         return (2.0 * Math.atan(Math.exp(Math.PI * y / 2.0))) / Math.PI;
   }

   public static double barF(double mu, double sigma, double x) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
 
      double y = (x - mu) / sigma;
      if (y >= ZLIMB)
         return 0.0;
      else if (y <= -ZLIMS)
         return 1.0;
      else
         return 2.0 / Math.PI * Math.atan(Math.exp(-Math.PI * y / 2.0));
   }

   public static double inverseF(double mu, double sigma, double u) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      if (u < 0.0 || u > 1.0)
         throw new IllegalArgumentException("u not in [0,1]");
 
      if (u >= 1.0)
         return Double.POSITIVE_INFINITY;
      else if (u <= 0.0)
         return Double.NEGATIVE_INFINITY;
      else
         return (mu + (2.0 * sigma / Math.PI * Math.log(Math.tan(Math.PI / 2.0 * u))));
   }

   public static double[] getMLE(double[] x, int n) {
      double sum;
 
      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];
 
      sum = 0.0;
      for (int i = 0; i < n; i++)
         sum += x[i];
      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(sum / (double) n);
 
      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 HyperbolicSecantDist getInstanceFromMLE(double[] x, int n) {
      double parameters[] = getMLE(x, n);
      return new HyperbolicSecantDist(parameters[0], parameters[1]);
   }

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

   public static double getVariance(double mu, double sigma) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
 
      return (sigma * sigma);
   }

   public static double getStandardDeviation(double mu, double sigma) {
      return Math.sqrt(HyperbolicSecantDist.getVariance(mu, sigma));
   }

   public double getMu() {
      return mu;
   }

   public double getSigma() {
      return sigma;
   }

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

   public double[] getParams() {
      double[] retour = { mu, sigma };
      return retour;
   }

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