TriangularDist.java

/*
 * Class:        TriangularDist
 * Description:  triangular 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 java.util.Arrays;

public class TriangularDist extends ContinuousDistribution {
   private double a;
   private double b;
   private double m;

   public TriangularDist() {
      setParams(0.0, 1.0, 0.5);
   }

   public TriangularDist(double m) {
      setParams(0.0, 1.0, m);
   }

   public TriangularDist(double a, double b, double m) {
      setParams(a, b, m);
   }
 
   public double density(double x) {
      return density(a, b, m, x);
   }
 
   public double cdf(double x) {
      return cdf(a, b, m, x);
   }
 
   public double barF(double x) {
      return barF(a, b, m, x);
   }
 
   public double inverseF(double u) {
      return inverseF(a, b, m, u);
   }
 
   public double getMean() {
      return TriangularDist.getMean(a, b, m);
   }
 
   public double getVariance() {
      return TriangularDist.getVariance(a, b, m);
   }
 
   public double getStandardDeviation() {
      return TriangularDist.getStandardDeviation(a, b, m);
   }

   public static double density(double a, double b, double m, double x) {
      if (m < a || m > b)
         throw new IllegalArgumentException("m is not in [a,b]");
      if (x < a || x > b)
         return 0.0;
      else if (x <= m && m != a)
         return 2.0 * (x - a) / ((b - a) * (m - a));
      else
         return 2.0 * (b - x) / ((b - a) * (b - m));
   }

   public static double cdf(double a, double b, double m, double x) {
      if (m < a || m > b)
         throw new IllegalArgumentException("m is not in [a,b]");
      if (x <= a)
         return 0.0;
      else if (x <= m && m != a)
         return (x - a) * (x - a) / ((b - a) * (m - a));
      else if (x < b)
         return 1.0 - (b - x) * (b - x) / ((b - a) * (b - m));
      else
         return 1.0;
   }

   public static double barF(double a, double b, double m, double x) {
      if (m < a || m > b)
         throw new IllegalArgumentException("m is not in [a,b]");
      if (x <= a)
         return 1.0;
      else if (x <= m && m != a)
         return 1.0 - (x - a) * (x - a) / ((b - a) * (m - a));
      else if (x < b)
         return (b - x) * (b - x) / ((b - a) * (b - m));
      else
         return 0.0;
   }

   public static double inverseF(double a, double b, double m, double u) {
      if (m < a || m > b)
         throw new IllegalArgumentException("m is not in [a,b]");
      if (u < 0.0 || u > 1.0)
         throw new IllegalArgumentException("u is not in [0,1]");
      if (u <= 0.0)
         return a;
      if (u >= 1.0)
         return b;
      // the code is taken and adapted from unuran
      // file /distributions/c_triangular_gen.c
      double h = (m - a) / (b - a);
      return u <= h && m != a ? a + Math.sqrt((b - a) * (m - a) * u) : b - Math.sqrt((b - a) * (b - m) * (1 - u));
   }

   public static double[] getMLE(double[] x, int n, double a, double b) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
      double[] Y = new double[n]; // sorted x[i]
      System.arraycopy(x, 0, Y, 0, n);
      Arrays.sort(Y);
 
      int rmax = -1;
      double prodmax = -1.0e300;
      final double ba = b - a;
      double z;
      int i;
      for (int r = 0; r < n; r++) {
         z = (Y[r] - a) / ba;
         if ((z <= (double) r / n) || (z >= (double) (r + 1) / n))
            continue; // MLE cannot be there
         double prod = 1.0;
         double d = Y[r] - a;
         for (i = 0; i < r; i++)
            prod *= (Y[i] - a) / d;
 
         d = b - Y[r];
         for (i = r + 1; i < n; i++)
            prod *= (b - Y[i]) / d;
 
         if (prod > prodmax) {
            prodmax = prod;
            rmax = r;
         }
      }
 
      if (rmax < 0)
         throw new UnsupportedOperationException("   data cannot fit a triangular distribution");
 
      double[] param = new double[1];
      param[0] = Y[rmax];
      return param;
   }

   public static TriangularDist getInstanceFromMLE(double[] x, int n, double a, double b) {
      double param[] = getMLE(x, n, a, b);
      return new TriangularDist(a, b, param[0]);
   }

   public static double getMean(double a, double b, double m) {
      if ((a == 0.0 && b == 1.0) && (m < 0 || m > 1))
         throw new IllegalArgumentException("m is not in [0,1]");
      else if (m < a || m > b)
         throw new IllegalArgumentException("m is not in [a,b]");
 
      return ((a + b + m) / 3.0);
   }

   public static double getVariance(double a, double b, double m) {
      if ((a == 0.0 && b == 1.0) && (m < 0 || m > 1))
         throw new IllegalArgumentException("m is not in [0,1]");
      else if (m < a || m > b)
         throw new IllegalArgumentException("m is not in [a,b]");
 
      return ((a * a + b * b + m * m - a * b - a * m - b * m) / 18.0);
   }

   public static double getStandardDeviation(double a, double b, double m) {
      return Math.sqrt(TriangularDist.getVariance(a, b, m));
   }

   public double getA() {
      return a;
   }

   public double getB() {
      return b;
   }

   public double getM() {
      return m;
   }

   public void setParams(double a, double b, double m) {
      if ((a == 0.0 && b == 1.0) && (m < 0 || m > 1))
         throw new IllegalArgumentException("m is not in [0,1]");
      else if (a >= b)
         throw new IllegalArgumentException("a >= b");
      else if (m < a || m > b)
         throw new IllegalArgumentException("m is not in [a,b]");
      this.a = a;
      this.b = b;
      this.m = m;
      supportA = a;
      supportB = b;
   }

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

   public String toString() {
      return getClass().getSimpleName() + " : a = " + a + ", b = " + b + ", m = " + m;
   }
 
}