NakagamiDist.java

/*
 * Class:        NakagamiDist
 * Description:  Nakagami 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;

public class NakagamiDist extends ContinuousDistribution {
   protected double a; // Location parameter
   protected double lambda; // Scale parameter
   protected double c; // Shape parameter
   private double factor;
   private double ratio; // Gamma(c + 1/2)/Gamma(c)

   public NakagamiDist(double a, double lambda, double c) {
      setParams(a, lambda, c);
   }
 
   public double density(double x) {
      if (x <= a)
         return 0.0;
      return 2.0 * Math.exp(factor + Math.log(x - a) * (2.0 * c - 1.0) - lambda * (x - a) * (x - a));
   }
 
   public double cdf(double x) {
      return cdf(a, lambda, c, x);
   }
 
   public double barF(double x) {
      return barF(a, lambda, c, x);
   }
 
   public double inverseF(double u) {
      return inverseF(a, lambda, c, u);
   }
 
   public double getMean() {
      return a + ratio / Math.sqrt(lambda);
   }
 
   public double getVariance() {
      return (c - ratio * ratio) / lambda;
   }
 
   public double getStandardDeviation() {
      return Math.sqrt(getVariance());
   }

   public static double density(double a, double lambda, double c, double x) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (c <= 0.0)
         throw new IllegalArgumentException("c <= 0");
      if (x <= a)
         return 0.0;
 
      return 2.0 * Math.exp(
            Math.log(lambda) * c - Num.lnGamma(c) + Math.log(x - a) * (2.0 * c - 1.0) - lambda * (x - a) * (x - a));
   }

   public static double cdf(double a, double lambda, double c, double x) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (c <= 0.0)
         throw new IllegalArgumentException("c <= 0");
      if (x <= a)
         return 0.0;
 
      return GammaDist.cdf(c, 12, lambda * (x - a) * (x - a));
   }

   public static double barF(double a, double lambda, double c, double x) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (c <= 0.0)
         throw new IllegalArgumentException("c <= 0");
      if (x <= a)
         return 1.0;
      return GammaDist.barF(c, 12, lambda * (x - a) * (x - a));
   }

   public static double inverseF(double a, double lambda, double c, double u) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (c <= 0.0)
         throw new IllegalArgumentException("c <= 0");
      if (u > 1.0 || u < 0.0)
         throw new IllegalArgumentException("u not in [0,1]");
      if (u <= 0.0)
         return a;
      if (u >= 1.0)
         return Double.POSITIVE_INFINITY;
      double res = GammaDist.inverseF(c, 12, u);
      return a + Math.sqrt(res / lambda);
   }

   public static double getMean(double a, double lambda, double c) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (c <= 0.0)
         throw new IllegalArgumentException("c <= 0");
      return a + Num.gammaRatioHalf(c) / Math.sqrt(lambda);
   }

   public static double getVariance(double a, double lambda, double c) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (c <= 0.0)
         throw new IllegalArgumentException("c <= 0");
      double rat = Num.gammaRatioHalf(c);
      return (c - rat * rat) / lambda;
   }

   public static double getStandardDeviation(double a, double lambda, double c) {
      return Math.sqrt(NakagamiDist.getVariance(a, lambda, c));
   }

   public double getA() {
      return a;
   }

   public double getLambda() {
      return lambda;
   }

   public double getC() {
      return c;
   }

   public void setParams(double a, double lambda, double c) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (c <= 0.0)
         throw new IllegalArgumentException("c <= 0");
      this.a = a;
      this.lambda = lambda;
      this.c = c;
      factor = (Math.log(lambda) * c - Num.lnGamma(c));
      ratio = Num.gammaRatioHalf(c);
   }

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

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