RayleighDist.java

/*
 * Class:        RayleighDist
 * Description:  Rayleigh 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;

public class RayleighDist extends ContinuousDistribution {
   private double a;
   private double beta;

   public RayleighDist(double beta) {
      setParams(0.0, beta);
   }

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

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

   public static double density(double beta, double x) {
      return density(0.0, beta, x);
   }

   public static double cdf(double a, double beta, double x) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (x <= a)
         return 0.0;
      final double Z = (x - a) / beta;
      if (Z >= 10.0)
         return 1.0;
      return -Math.expm1(-Z * Z / 2.0);
   }

   public static double cdf(double beta, double x) {
      return cdf(0.0, beta, x);
   }

   public static double barF(double a, double beta, double x) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (x <= a)
         return 1.0;
      double z = (x - a) / beta;
      if (z >= 44.0)
         return 0.0;
      return Math.exp(-z * z / 2.0);
   }

   public static double barF(double beta, double x) {
      return barF(0.0, beta, x);
   }

   public static double inverseF(double a, double beta, double u) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (u < 0.0 || u > 1.0)
         throw new IllegalArgumentException("u not in [0, 1]");
      if (u <= 0.0)
         return a;
      if (u >= 1.0)
         return Double.POSITIVE_INFINITY;
 
      return a + beta * Math.sqrt(-2.0 * Math.log1p(-u));
   }

   public static double inverseF(double beta, double u) {
      return inverseF(0.0, beta, u);
   }

   public static double[] getMLE(double[] x, int n, double a) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
 
      double somme = 0;
      for (int i = 0; i < n; ++i)
         somme += (x[i] - a) * (x[i] - a);
 
      double[] parametres = new double[1];
      parametres[0] = Math.sqrt(somme / (2.0 * n));
      return parametres;
   }

   public static RayleighDist getInstanceFromMLE(double[] x, int n, double a) {
      double parameters[] = getMLE(x, n, a);
      return new RayleighDist(parameters[0], parameters[1]);
   }

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

   public static double getVariance(double beta) {
      if (beta == 0.0)
         throw new IllegalArgumentException("beta = 0");
      return (2.0 - 0.5 * Math.PI) * beta * beta;
   }

   public static double getStandardDeviation(double beta) {
      return Math.sqrt(RayleighDist.getVariance(beta));
   }

   public double getA() {
      return a;
   }

   public double getSigma() {
      return beta;
   }

   public void setParams(double a, double beta) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      this.a = a;
      this.beta = beta;
      supportA = a;
   }

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

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