TruncatedDist.java

/*
 * Class:        TruncatedDist
 * Description:  an arbitrary continuous distribution truncated
 * Environment:  Java
 * Software:     SSJ
 * Copyright (C) 2001  Pierre L'Ecuyer and Universite de Montreal
 * Organization: DIRO, Universite de Montreal
 * @author       Richard Simard
 * @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.functions.MathFunctionUtil;
import umontreal.ssj.functions.MathFunction;

public class TruncatedDist extends ContinuousDistribution {
   public static int NUMINTERVALS = 500;
 
   private ContinuousDistribution dist0; // The original (non-truncated) dist.
   private double fa; // F(a)
   private double fb; // F(b)
   private double barfb; // bar F(b)
   private double fbfa; // F(b) - F(a)
   private double a;
   private double b;
   private double approxMean;
   private double approxVariance;
   private double approxStandardDeviation;

   public TruncatedDist(ContinuousDistribution dist, double a, double b) {
      setParams(dist, a, b);
   }
 
   public double density(double x) {
      if ((x < a) || (x > b))
         return 0;
      return dist0.density(x) / fbfa;
   }
 
   public double cdf(double x) {
      if (x <= a)
         return 0;
      else if (x >= b)
         return 1;
      else
         return (dist0.cdf(x) - fa) / fbfa;
   }
 
   public double barF(double x) {
      if (x <= a)
         return 1;
      else if (x >= b)
         return 0;
      else
         return (dist0.barF(x) - barfb) / fbfa;
   }
 
   public double inverseF(double u) {
      if (u == 0)
         return a;
      if (u == 1)
         return b;
      return dist0.inverseF(fa + fbfa * u);
   }

   public double getMean() {
      if (Double.isNaN(approxMean))
         throw new UnsupportedOperationException("Undefined mean");
      return approxMean;
   }

   public double getVariance() {
      if (Double.isNaN(approxVariance))
         throw new UnsupportedOperationException("Unknown variance");
      return approxVariance;
   }

   public double getStandardDeviation() {
      if (Double.isNaN(approxStandardDeviation))
         throw new UnsupportedOperationException("Unknown standard deviation");
      return approxStandardDeviation;
   }

   public double getA() {
      return a;
   }

   public double getB() {
      return b;
   }

   public double getFa() {
      return fa;
   }

   public double getFb() {
      return fb;
   }

   public double getArea() {
      return fbfa;
   }

   public void setParams(ContinuousDistribution dist, double a, double b) {
      if (a >= b)
         throw new IllegalArgumentException("a must be smaller than b.");
      this.dist0 = dist;
      if (a < dist.getXinf())
         a = dist.getXinf();
      if (b > dist.getXsup())
         b = dist.getXsup();
      supportA = this.a = a;
      supportB = this.b = b;
      fa = dist.cdf(a);
      fb = dist.cdf(b);
      fbfa = fb - fa;
      barfb = dist.barF(b);
 
      if (((a <= dist.getXinf()) && (b >= dist.getXsup()))
            || ((a == Double.NEGATIVE_INFINITY) && (b == Double.POSITIVE_INFINITY))) {
         approxMean = dist.getMean();
         approxVariance = dist.getVariance();
         approxStandardDeviation = dist.getStandardDeviation();
 
      } else {
         // The mean is the integral of xf*(x) over [a, b].
         MomentFunction func1 = new MomentFunction(dist, 1);
         approxMean = MathFunctionUtil.simpsonIntegral(func1, a, b, NUMINTERVALS) / fbfa;
 
         // Estimate the integral of (x-E[X])^2 f*(x) over [a, b]
         MomentFunction func2 = new MomentFunction(dist, 2, approxMean);
         approxVariance = MathFunctionUtil.simpsonIntegral(func2, a, b, NUMINTERVALS) / fbfa;
 
         approxStandardDeviation = Math.sqrt(approxVariance);
      }
   }

   public double[] getParams() {
      double[] retour = { a, b, fa, fb, fbfa };
      return retour;
   }

   public String toString() {
      return getClass().getSimpleName() + " : a = " + a + ", b = " + b + ", F(a) = " + fa + ", F(b) = " + fb
            + ", F(b)-F(a) = " + fbfa;
   }
 
   private static class MomentFunction implements MathFunction {
      private ContinuousDistribution dist;
      private int moment;
      private double offset;
 
      public MomentFunction(ContinuousDistribution dist, int moment) {
         this.dist = dist;
         this.moment = moment;
         offset = 0;
      }
 
      public MomentFunction(ContinuousDistribution dist, int moment, double offset) {
         this(dist, moment);
         this.offset = offset;
      }
 
      public double evaluate(double x) {
         double res = dist.density(x);
         final double offsetX = x - offset;
         for (int i = 0; i < moment; i++)
            res *= offsetX;
         return res;
      }
   }
}