InverseGaussianDist.java

/*
 * Class:        InverseGaussianDist
 * Description:  inverse Gaussian 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.probdist.NormalDist;
import umontreal.ssj.util.*;
import umontreal.ssj.functions.MathFunction;

public class InverseGaussianDist extends ContinuousDistribution {
   protected double mu;
   protected double lambda;
 
   private static class Function implements MathFunction {
      protected double mu;
      protected double lambda;
      protected double u;
 
      public Function(double mu, double lambda, double u) {
         this.mu = mu;
         this.lambda = lambda;
         this.u = u;
      }
 
      public double evaluate(double x) {
         return u - cdf(mu, lambda, x);
      }
   }

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

   public static double density(double mu, double lambda, double x) {
      if (mu <= 0.0)
         throw new IllegalArgumentException("mu <= 0");
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (x <= 0.0)
         return 0.0;
 
      double sqrtX = Math.sqrt(x);
 
      return (Math.sqrt(lambda / (2 * Math.PI)) / (sqrtX * sqrtX * sqrtX)
            * Math.exp(-lambda * (x - 2 * mu + (mu * mu / x)) / (2 * mu * mu)));
   }

   public static double cdf(double mu, double lambda, double x) {
      if (mu <= 0.0)
         throw new IllegalArgumentException("mu <= 0");
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (x <= 0.0)
         return 0.0;
      double temp = Math.sqrt(lambda / x);
      double z = temp * (x / mu - 1.0);
      double w = temp * (x / mu + 1.0);
 
      // C'est bien un + dans exp (2 * lambda / mu)
      return (NormalDist.cdf01(z) + Math.exp(2 * lambda / mu) * NormalDist.cdf01(-w));
   }

   public static double barF(double mu, double lambda, double x) {
      return 1.0 - cdf(mu, lambda, x);
   }

   public static double inverseF(double mu, double lambda, double u) {
      if (mu <= 0.0)
         throw new IllegalArgumentException("mu <= 0");
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (u < 0.0 || u > 1.0)
         throw new IllegalArgumentException("u must be in [0,1]");
      if (u == 1.0)
         return Double.POSITIVE_INFINITY;
      if (u == 0.0)
         return 0.0;
 
      Function f = new Function(mu, lambda, u);
 
      // Find interval containing root = x*
      double sig = getStandardDeviation(mu, lambda);
      double x0 = 0.0;
      double x = mu;
      double v = cdf(mu, lambda, x);
      while (v < u) {
         x0 = x;
         x += 3.0 * sig;
         v = cdf(mu, lambda, x);
      }
 
      return RootFinder.brentDekker(x0, x, f, 1e-12);
   }

   public static double[] getMLE(double[] x, int n) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
 
      double parameters[];
      parameters = new double[2];
      double sum = 0;
      for (int i = 0; i < n; i++) {
         sum += x[i];
      }
      parameters[0] = sum / (double) n;
 
      sum = 0;
      for (int i = 0; i < n; i++) {
         sum += ((1.0 / (double) x[i]) - (1.0 / parameters[0]));
      }
      parameters[1] = (double) n / (double) sum;
 
      return parameters;
   }

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

   public static double getMean(double mu, double lambda) {
      if (mu <= 0.0)
         throw new IllegalArgumentException("mu <= 0");
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
 
      return mu;
   }

   public static double getVariance(double mu, double lambda) {
      if (mu <= 0.0)
         throw new IllegalArgumentException("mu <= 0");
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
 
      return (mu * mu * mu / lambda);
   }

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

   public double getLambda() {
      return lambda;
   }

   public double getMu() {
      return mu;
   }

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

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

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