FatigueLifeDist.java

/*
 * Class:        FatigueLifeDist
 * Description:  fatigue life 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 optimization.*;

public class FatigueLifeDist extends ContinuousDistribution {
   protected double mu;
   protected double beta;
   protected double gamma;
 
   private static class Optim implements Uncmin_methods {
      private int n;
      private double[] xi;
      private double mu;
 
      public Optim(double[] x, int n, double min) {
         this.n = n;
         this.mu = min;
         this.xi = new double[n];
         System.arraycopy(x, 0, this.xi, 0, n);
      }
 
      public double f_to_minimize(double[] p) {
         double sum = 0.0;
 
         if ((p[1] <= 0.0) || (p[2] <= 0.0))
            return 1e200;
 
         for (int i = 0; i < n; i++)
            sum -= Math.log(density(mu, p[1], p[2], xi[i]));
 
         return sum;
      }
 
      public void gradient(double[] x, double[] g) {
      }
 
      public void hessian(double[] x, double[][] h) {
      }
   }

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

   public static double density(double mu, double beta, double gamma, double x) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (gamma <= 0.0)
         throw new IllegalArgumentException("gamma <= 0");
      if (x <= mu)
         return 0.0;
      double y;
      y = (Math.sqrt((x - mu) / beta) - Math.sqrt(beta / (x - mu))) / gamma;
 
      return (((Math.sqrt((x - mu) / beta) + Math.sqrt(beta / (x - mu))) / (2 * gamma * (x - mu)))
            * NormalDist.density(0.0, 1.0, y));
   }

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

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

   public static double inverseF(double mu, double beta, double gamma, double u) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (gamma <= 0.0)
         throw new IllegalArgumentException("gamma <= 0");
      if (u > 1.0 || u < 0.0)
         throw new IllegalArgumentException("u not in [0,1]");
      if (u <= 0.0) // if u == 0, in fact
         return mu;
      if (u >= 1.0) // if u == 1, in fact
         return Double.POSITIVE_INFINITY;
 
      double w = gamma * NormalDist.inverseF01(u);
      double sqrtZ = 0.5 * (w + Math.sqrt(w * w + 4.0));
 
      return (mu + sqrtZ * sqrtZ * beta);
   }

   public static double[] getMLE(double[] x, int n, double mu) {
      double sum = 0.0;
 
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
 
      double[] parameters = new double[3];
      double[] xpls = new double[3];
      double[] param = new double[3];
      double[] fpls = new double[3];
      double[] gpls = new double[3];
      int[] itrcmd = new int[2];
      double[][] h = new double[3][3];
      double[] udiag = new double[3];
 
      Optim system = new Optim(x, n, mu);
 
      double mean = 0.0;
      for (int i = 0; i < n; i++)
         mean += x[i];
      mean /= (double) n;
 
      double var = 0.0;
      for (int i = 0; i < n; i++)
         var += (x[i] - mean) * (x[i] - mean);
      var /= (double) n;
 
      double loc2 = (mean - mu) * (mean - mu);
      double a = 0.25 * (var - 5 * loc2);
      double b = (var - loc2);
      double c = var;
 
      double delta = b * b - 4.0 * a * c;
 
      double gamma2 = (-b - Math.sqrt(delta)) / (2.0 * a);
      param[2] = Math.sqrt(gamma2);
      param[1] = (mean - mu) / (1.0 + gamma2 / 2.0);
 
      Uncmin_f77.optif0_f77(2, param, system, xpls, fpls, gpls, itrcmd, h, udiag);
 
      for (int i = 1; i < 3; i++)
         parameters[i] = xpls[i];
      parameters[0] = mu;
      return parameters;
   }

   public static double getMean(double mu, double beta, double gamma) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (gamma <= 0.0)
         throw new IllegalArgumentException("gamma <= 0");
 
      return (mu + beta * (1 + 0.5 * gamma * gamma));
   }

   public static double getVariance(double mu, double beta, double gamma) {
      if (beta <= 0.0)
         throw new IllegalArgumentException("beta <= 0");
      if (gamma <= 0.0)
         throw new IllegalArgumentException("gamma <= 0");
 
      return (beta * beta * gamma * gamma * (1.0 + 5.0 / 4.0 * gamma * gamma));
   }

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

   public double getBeta() {
      return beta;
   }

   public double getGamma() {
      return gamma;
   }

   public double getMu() {
      return mu;
   }

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

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

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