HalfNormalDist.java

/*
 * Class:        HalfNormalDist
 * Description:  half-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 HalfNormalDist extends ContinuousDistribution {
   protected double mu;
   protected double sigma;
   protected double C1;

   public HalfNormalDist(double mu, double sigma) {
      setParams(mu, sigma);
   }
 
   public double density(double x) {
      final double z = (x - mu) / sigma;
      if (z < 0.0)
         return 0.0;
      return C1 * Math.exp(-z * z / 2.0);
   }
 
   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 HalfNormalDist.getMean(mu, sigma);
   }
 
   public double getVariance() {
      return HalfNormalDist.getVariance(mu, sigma);
   }
 
   public double getStandardDeviation() {
      return HalfNormalDist.getStandardDeviation(mu, sigma);
   }

   public static double density(double mu, double sigma, double x) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      final double Z = (x - mu) / sigma;
      if (Z < 0.0)
         return 0.0;
      return Math.sqrt(2.0 / Math.PI) / sigma * Math.exp(-Z * Z / 2.0);
   }

   public static double cdf(double mu, double sigma, double x) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      final double Z = (x - mu) / sigma;
      if (Z <= 0.0)
         return 0.0;
      return Num.erf(Z / Num.RAC2);
   }

   public static double barF(double mu, double sigma, double x) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      final double Z = (x - mu) / sigma;
      if (Z <= 0.0)
         return 1.0;
      return Num.erfc(Z / Num.RAC2);
   }

   public static double inverseF(double mu, double sigma, double u) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      if (u > 1.0 || u < 0.0)
         throw new IllegalArgumentException("u not in [0,1]");
      if (u <= 0.0)
         return mu;
      if (u >= 1.0)
         return Double.POSITIVE_INFINITY;
 
      final double Z = Num.RAC2 * Num.erfInv(u);
      return mu + sigma * Z;
   }

   public static double[] getMLE(double[] x, int n) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
 
      double mu = Double.MAX_VALUE;
      for (int i = 0; i < n; ++i)
         if (x[i] < mu)
            mu = x[i];
 
      double sigma = 0.0;
      for (int i = 0; i < n; ++i)
         sigma += (x[i] - mu) * (x[i] - mu);
 
      double[] parametres = new double[2];
      parametres[0] = mu;
      parametres[1] = Math.sqrt(sigma / n);
      return parametres;
   }

   public static double[] getMLE(double[] x, int n, double mu) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
 
      double sigma = 0.0;
      for (int i = 0; i < n; ++i)
         sigma += (x[i] - mu) * (x[i] - mu);
 
      double[] parametres = new double[1];
      parametres[0] = Math.sqrt(sigma / n);
      return parametres;
   }

   public static double getMean(double mu, double sigma) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      return mu + sigma * Math.sqrt(2.0 / Math.PI);
   }

   public static double getVariance(double mu, double sigma) {
      if (sigma <= 0.0)
         throw new IllegalArgumentException("sigma <= 0");
      return (1.0 - 2.0 / Math.PI) * sigma * sigma;
   }

   public static double getStandardDeviation(double mu, double sigma) {
      return Math.sqrt(HalfNormalDist.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;
      C1 = Math.sqrt(2.0 / Math.PI) / sigma;
   }

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

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