WeibullDist.java

/*
 * Class:        WeibullDist
 * Description:  Weibull 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;
import umontreal.ssj.util.RootFinder;
import umontreal.ssj.functions.MathFunction;

public class WeibullDist extends ContinuousDistribution {
   private double alpha;
   private double lambda;
   private double delta;
 
   private static class Function implements MathFunction {
      private int n;
      private double xi[];
      private double lnXi[];
      private double sumLnXi = 0.0;
      private final double LN_EPS = Num.LN_DBL_MIN - Num.LN2;
 
      public Function(double x[], int n) {
         this.n = n;
         this.xi = new double[n];
         this.lnXi = new double[n];
 
         for (int i = 0; i < n; i++) {
            this.xi[i] = x[i];
            if (x[i] > 0.0)
               this.lnXi[i] = Math.log(x[i]);
            else
               this.lnXi[i] = LN_EPS;
            sumLnXi += this.lnXi[i];
         }
      }
 
      public double evaluate(double x) {
         if (x <= 0.0)
            return 1.0e200;
         double sumXiLnXi = 0.0;
         double sumXi = 0.0;
         double xalpha;
 
         for (int i = 0; i < n; i++) {
            xalpha = Math.pow(this.xi[i], x);
            sumXiLnXi += xalpha * lnXi[i];
            sumXi += xalpha;
         }
 
         return (x * (n * sumXiLnXi - sumLnXi * sumXi) - n * sumXi);
      }
   }

   public WeibullDist(double alpha) {
      setParams(alpha, 1.0, 0.0);
   }

   public WeibullDist(double alpha, double lambda, double delta) {
      setParams(alpha, lambda, delta);
   }
 
   public double density(double x) {
      return density(alpha, lambda, delta, x);
   }
 
   public double cdf(double x) {
      return cdf(alpha, lambda, delta, x);
   }
 
   public double barF(double x) {
      return barF(alpha, lambda, delta, x);
   }
 
   public double inverseF(double u) {
      return inverseF(alpha, lambda, delta, u);
   }
 
   public double getMean() {
      return WeibullDist.getMean(alpha, lambda, delta);
   }
 
   public double getVariance() {
      return WeibullDist.getVariance(alpha, lambda, delta);
   }
 
   public double getStandardDeviation() {
      return WeibullDist.getStandardDeviation(alpha, lambda, delta);
   }

   public static double density(double alpha, double lambda, double delta, double x) {
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 0");
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (x <= delta)
         return 0.0;
      double y = Math.log(lambda * (x - delta)) * alpha;
      if (y >= 7.0)
         return 0.0;
      y = Math.exp(y);
 
      return alpha * (y / (x - delta)) * Math.exp(-y);
   }

   public static double density(double alpha, double x) {
      return density(alpha, 1.0, 0.0, x);
   }

   public static double cdf(double alpha, double lambda, double delta, double x) {
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 0");
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (x <= delta)
         return 0.0;
      if ((lambda * (x - delta) >= XBIG) && (alpha >= 1.0))
         return 1.0;
      double y = Math.log(lambda * (x - delta)) * alpha;
      if (y >= 3.65)
         return 1.0;
      y = Math.exp(y);
      return -Math.expm1(-y); // in JDK-1.5
   }

   public static double cdf(double alpha, double x) {
      return cdf(alpha, 1.0, 0.0, x);
   }

   public static double barF(double alpha, double lambda, double delta, double x) {
      if (alpha <= 0)
         throw new IllegalArgumentException("alpha <= 0");
      if (lambda <= 0)
         throw new IllegalArgumentException("lambda <= 0");
      if (x <= delta)
         return 1.0;
      if (alpha >= 1.0 && x >= Num.DBL_MAX_EXP * 2)
         return 0.0;
 
      double temp = Math.log(lambda * (x - delta)) * alpha;
      if (temp >= Num.DBL_MAX_EXP * Num.LN2)
         return 0.0;
      temp = Math.exp(temp);
      return Math.exp(-temp);
   }

   public static double barF(double alpha, double x) {
      return barF(alpha, 1.0, 0.0, x);
   }

   public static double inverseF(double alpha, double lambda, double delta, double u) {
      double t;
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 0");
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
 
      if (u < 0.0 || u > 1.0)
         throw new IllegalArgumentException("u not in [0, 1]");
      if (u <= 0.0)
         return 0.0;
      if (u >= 1.0)
         return Double.POSITIVE_INFINITY;
 
      t = -Math.log1p(-u);
      if (Math.log(t) / Math.log(10) >= alpha * Num.DBL_MAX_10_EXP)
         throw new ArithmeticException("inverse function cannot be positive infinity");
 
      return Math.pow(t, 1.0 / alpha) / lambda + delta;
   }

   public static double inverseF(double alpha, double x) {
      return inverseF(alpha, 1.0, 0.0, x);
   }
 
   private static double[] getMaximumLikelihoodEstimate(double[] x, int n, double delta) {
      if (n <= 0)
         throw new IllegalArgumentException("n <= 0");
      if (delta != 0.0)
         throw new IllegalArgumentException("delta must be equal to 0");
// Verifier cette fonction si delta != 0.
 
      final double LN_EPS = Num.LN_DBL_MIN - Num.LN2;
      double sumLn = 0.0;
      double sumLn2 = 0.0;
      double lnxi;
      for (int i = 0; i < n; i++) {
         if (x[i] <= delta)
            lnxi = LN_EPS;
         else
            lnxi = Math.log(x[i]);
         sumLn += lnxi;
         sumLn2 += lnxi * lnxi;
      }
 
      double alpha0 = Math.sqrt((double) n / ((6.0 / (Math.PI * Math.PI)) * (sumLn2 - sumLn * sumLn / (double) n)));
      double a = alpha0 - 20.0;
      if (a <= delta)
         a = delta + 1.0e-5;
 
      double param[] = new double[3];
      param[2] = 0.0;
      Function f = new Function(x, n);
      param[0] = RootFinder.brentDekker(a, alpha0 + 20.0, f, 1e-5);
 
      double sumXalpha = 0.0;
      for (int i = 0; i < n; i++)
         sumXalpha += Math.pow(x[i], param[0]);
      param[1] = Math.pow((double) n / sumXalpha, 1.0 / param[0]);
 
      return param;
   }

   public static double[] getMLE(double[] x, int n) {
      return getMaximumLikelihoodEstimate(x, n, 0.0);
   }

   public static WeibullDist getInstanceFromMLE(double[] x, int n) {
      double param[] = getMLE(x, n);
      return new WeibullDist(param[0], param[1], param[2]);
   }

   public static double getMean(double alpha, double lambda, double delta) {
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 0");
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
 
      return (delta + Math.exp(Num.lnGamma(1.0 + 1.0 / alpha)) / lambda);
   }

   public static double getVariance(double alpha, double lambda, double delta) {
      double gAlpha;
 
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 0");
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
 
      gAlpha = Math.exp(Num.lnGamma(1.0 / alpha + 1.0));
 
      return (Math.abs(Math.exp(Num.lnGamma(2 / alpha + 1)) - gAlpha * gAlpha) / (lambda * lambda));
   }

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

   public double getAlpha() {
      return alpha;
   }

   public double getLambda() {
      return lambda;
   }

   public double getDelta() {
      return delta;
   }

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

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

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