FoldedNormalDist.java

/*
 * Class:        FoldedNormalDist
 * Description:  folded normal 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.*;
import umontreal.ssj.functions.MathFunction;
import optimization.*;

public class FoldedNormalDist extends ContinuousDistribution {
   protected double mu;
   protected double sigma;
   private static final double RACPI = 1.7724538509055160273; // Sqrt[PI]
 
   private static class FunctionInverse implements MathFunction {
      private double u, mu, sigma;
 
      public FunctionInverse(double mu, double sigma, double u) {
         this.u = u;
         this.mu = mu;
         this.sigma = sigma;
      }
 
      public double evaluate(double x) {
         return u - cdf(mu, sigma, x);
      }
   }

   public FoldedNormalDist(double mu, double sigma) {
      setParams(mu, sigma);
   }
 
   public double density(double x) {
      return density(mu, sigma, x);
   }
 
   public double cdf(double x) {
      return cdf(mu, sigma, x);
   }
 
   public double barF(double x) {
      return barF(mu, sigma, x);
   }
 
   public double inverseF(double u) {
      return inverseF(mu, sigma, u);
   }
 
   public double getMean() {
      return FoldedNormalDist.getMean(mu, sigma);
   }
 
   public double getVariance() {
      return FoldedNormalDist.getVariance(mu, sigma);
   }
 
   public double getStandardDeviation() {
      return FoldedNormalDist.getStandardDeviation(mu, sigma);
   }

   public static double density(double mu, double sigma, double x) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      if (mu < 0.0)
         throw new IllegalArgumentException("mu < 0");
      if (x < 0.0)
         return 0.0;
      return NormalDist.density(mu, sigma, x) + NormalDist.density(mu, sigma, -x);
   }

   public static double cdf(double mu, double sigma, double x) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      if (mu < 0.0)
         throw new IllegalArgumentException("mu < 0");
      if (x <= 0.0)
         return 0.0;
      return NormalDist.cdf01((x - mu) / sigma) - NormalDist.cdf01((-x - mu) / sigma);
   }

   public static double barF(double mu, double sigma, double x) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      if (mu < 0.0)
         throw new IllegalArgumentException("mu < 0");
      if (x <= 0.0)
         return 1.0;
      return NormalDist.barF01((x - mu) / sigma) - NormalDist.barF01((-x - mu) / sigma);
   }

   public static double inverseF(double mu, double sigma, double u) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      if (mu < 0.0)
         throw new IllegalArgumentException("mu < 0");
      if (u > 1.0 || u < 0.0)
         throw new IllegalArgumentException("u not in [0,1]");
      if (u <= 0.0)
         return 0.0;
      if (u >= 1.0)
         return Double.POSITIVE_INFINITY;
 
      MathFunction f = new FunctionInverse(mu, sigma, u);
      return RootFinder.brentDekker(0.0, mu + 10.0 * sigma, f, 1.0e-14);
   }

   public static double getMean(double mu, double sigma) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      if (mu < 0.0)
         throw new IllegalArgumentException("mu < 0");
 
      return sigma * Num.RAC2 / RACPI * Math.exp(-mu * mu / (2.0 * sigma * sigma))
            + mu * Num.erf(mu / (sigma * Num.RAC2));
   }

   public static double getVariance(double mu, double sigma) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      if (mu < 0.0)
         throw new IllegalArgumentException("mu < 0");
      double mean = sigma * Num.RAC2 / RACPI * Math.exp(-mu * mu / (2.0 * sigma * sigma))
            + mu * Num.erf(mu / (sigma * Num.RAC2));
      return mu * mu + sigma * sigma - mean * mean;
   }

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

   public static double[] getMLE(double[] x, int n) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
      throw new UnsupportedOperationException("getMLE is not implemented ");
   }

   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");
      if (mu < 0.0)
         throw new IllegalArgumentException("mu < 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;
   }
 
}