ChiDist.java

/*
 * Class:        ChiDist
 * Description:  chi 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.functions.MathFunction;

public class ChiDist extends ContinuousDistribution {
   private int nu;
   private double C1;
 
   private static class Function implements MathFunction {
      protected int n;
      protected double sum;
 
      public Function(double s, int n) {
         this.n = n;
         this.sum = s;
      }
 
      public double evaluate(double k) {
         if (k < 1.0)
            return 1.0e200;
         return (sum + n * (Num.lnGamma(k / 2.0) - 0.5 * (Num.LN2) - Num.lnGamma((k + 1.0) / 2.0)));
      }
   }

   public ChiDist(int nu) {
      setNu(nu);
   }
 
   public double density(double x) {
      if (x <= 0.0)
         return 0.0;
      return Math.exp((nu - 1) * Math.log(x) - x * x / 2.0 - C1);
   }
 
   public double cdf(double x) {
      return cdf(nu, x);
   }
 
   public double barF(double x) {
      return barF(nu, x);
   }
 
   public double inverseF(double u) {
      return inverseF(nu, u);
   }
 
   public double getMean() {
      return ChiDist.getMean(nu);
   }
 
   public double getVariance() {
      return ChiDist.getVariance(nu);
   }
 
   public double getStandardDeviation() {
      return ChiDist.getStandardDeviation(nu);
   }

   public static double density(int nu, double x) {
      if (nu <= 0)
         throw new IllegalArgumentException("nu <= 0");
      if (x <= 0.0)
         return 0.0;
      return Math.exp((nu - 1) * Math.log(x) - x * x / 2.0 - (nu / 2.0 - 1.0) * Num.LN2 - Num.lnGamma(nu / 2.0));
   }

   public static double cdf(int nu, double x) {
      if (x <= 0.0)
         return 0.0;
      return GammaDist.cdf(nu / 2.0, 15, x * x / 2.0);
   }

   public static double barF(int nu, double x) {
      if (x <= 0.0)
         return 1.0;
      return GammaDist.barF(nu / 2.0, 15, x * x / 2.0);
   }

   public static double inverseF(int nu, double u) {
      double res = GammaDist.inverseF(nu / 2.0, 15, u);
      return Math.sqrt(2 * res);
   }

   public static double[] getMLE(double[] x, int n) {
      double[] parameters = new double[1];
 
      double mean = 0.0;
      for (int i = 0; i < n; i++)
         mean += x[i];
      mean /= (double) n;
 
      double var = 0.0;
      for (int i = 0; i < n; i++)
         var += ((x[i] - mean) * (x[i] - mean));
      var /= (double) n;
 
      double k = Math.round(var + mean * mean) - 5.0;
      if (k < 1.0)
         k = 1.0;
 
      double sum = 0.0;
      for (int i = 0; i < n; i++) {
         if (x[i] > 0.0)
            sum += Math.log(x[i]);
         else
            sum -= 709.0;
      }
 
      Function f = new Function(sum, n);
      while (f.evaluate(k) > 0.0)
         k++;
      parameters[0] = k;
 
      return parameters;
   }

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

   public static double getMean(int nu) {
      if (nu <= 0)
         throw new IllegalArgumentException("nu <= 0");
      return Num.RAC2 * Num.gammaRatioHalf(nu / 2.0);
   }

   public static double getVariance(int nu) {
      if (nu <= 0)
         throw new IllegalArgumentException("nu <= 0");
      double mean = ChiDist.getMean(nu);
      return (nu - (mean * mean));
   }

   public static double getStandardDeviation(int nu) {
      return Math.sqrt(ChiDist.getVariance(nu));
   }

   public int getNu() {
      return nu;
   }

   public void setNu(int nu) {
      if (nu <= 0)
         throw new IllegalArgumentException("nu <= 0");
      this.nu = nu;
      supportA = 0.0;
      C1 = (nu / 2.0 - 1.0) * Num.LN2 + Num.lnGamma(nu / 2.0);
   }

   public double[] getParams() {
      double[] retour = { nu };
      return retour;
   }

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