JohnsonSUDist.java

/*
 * Class:        JohnsonSUDist
 * Description:  Johnson S_U 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 JohnsonSUDist extends JohnsonSystem {
 
   private static double calcR(double a, double b, double x) {
      /***
       * cette fonction calcule r = z + sqrt(z*z + 1) en utilisant un algorithme
       * stable
       ***/
 
      double z = (x - a) / b;
 
      double s = Math.abs(z);
      if (s < 1.0e20)
         s = Math.sqrt(z * z + 1.0);
 
      // compute r = z + sqrt (z * z + 1)
      double r;
      if (z >= 0.0)
         r = s + z;
      else
         r = 1.0 / (s - z);
 
      return r;
   }

   public JohnsonSUDist(double gamma, double delta) {
      this(gamma, delta, 0, 1);
   }

   public JohnsonSUDist(double gamma, double delta, double xi, double lambda) {
      super(gamma, delta, xi, lambda);
   }
 
   public double density(double x) {
      return density(gamma, delta, xi, lambda, x);
   }
 
   public double cdf(double x) {
      return cdf(gamma, delta, xi, lambda, x);
   }
 
   public double barF(double x) {
      return barF(gamma, delta, xi, lambda, x);
   }
 
   public double inverseF(double u) {
      return inverseF(gamma, delta, xi, lambda, u);
   }
 
   public double getMean() {
      return JohnsonSUDist.getMean(gamma, delta, xi, lambda);
   }
 
   public double getVariance() {
      return JohnsonSUDist.getVariance(gamma, delta, xi, lambda);
   }
 
   public double getStandardDeviation() {
      return JohnsonSUDist.getStandardDeviation(gamma, delta, xi, lambda);
   }

   public static double density(double gamma, double delta, double xi, double lambda, double x) {
      if (lambda <= 0)
         throw new IllegalArgumentException("lambda <= 0");
      if (delta <= 0)
         throw new IllegalArgumentException("delta <= 0");
      double r = calcR(xi, lambda, x);
      if (r <= 0.0)
         return 0.0;
      double z = gamma + delta * Math.log(r);
      double y = (x - xi) / lambda;
      if (z >= 1.0e10)
         return 0;
      return delta / (lambda * Math.sqrt(2.0 * Math.PI) * Math.sqrt(y * y + 1.0)) * Math.exp(-z * z / 2.0);
   }

   public static double cdf(double gamma, double delta, double xi, double lambda, double x) {
      if (lambda <= 0)
         throw new IllegalArgumentException("lambda <= 0");
      if (delta <= 0)
         throw new IllegalArgumentException("delta <= 0");
      double r = calcR(xi, lambda, x);
      if (r > 0.0)
         return NormalDist.cdf01(gamma + delta * Math.log(r));
      else
         return 0.0;
   }

   public static double barF(double gamma, double delta, double xi, double lambda, double x) {
      if (lambda <= 0)
         throw new IllegalArgumentException("lambda <= 0");
      if (delta <= 0)
         throw new IllegalArgumentException("delta <= 0");
 
      double r = calcR(xi, lambda, x);
      if (r > 0.0)
         return NormalDist.barF01(gamma + delta * Math.log(r));
      else
         return 1.0;
   }

   public static double inverseF(double gamma, double delta, double xi, double lambda, double u) {
      if (lambda <= 0)
         throw new IllegalArgumentException("lambda <= 0");
      if (delta <= 0)
         throw new IllegalArgumentException("delta <= 0");
      if (u > 1.0 || u < 0.0)
         throw new IllegalArgumentException("u not in [0,1]");
 
      if (u >= 1.0)
         return Double.POSITIVE_INFINITY;
      if (u <= 0.0)
         return Double.NEGATIVE_INFINITY;
 
      double z = NormalDist.inverseF01(u);
      double v = (z - gamma) / delta;
      if (v >= Num.DBL_MAX_EXP * Num.LN2)
         return Double.POSITIVE_INFINITY;
      if (v <= Num.LN2 * Num.DBL_MIN_EXP)
         return Double.NEGATIVE_INFINITY;
 
      return xi + lambda * Math.sinh(v);
   }

   public static double getMean(double gamma, double delta, double xi, double lambda) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (delta <= 0.0)
         throw new IllegalArgumentException("delta <= 0");
 
      return (xi - (lambda * Math.exp(1.0 / (2.0 * delta * delta)) * Math.sinh(gamma / delta)));
   }

   public static double getVariance(double gamma, double delta, double xi, double lambda) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException("lambda <= 0");
      if (delta <= 0.0)
         throw new IllegalArgumentException("delta <= 0");
 
      double omega2 = Math.exp(1 / (delta * delta));
      return ((omega2 - 1) * (omega2 * Math.cosh(2 * gamma / delta) + 1) / 2 * lambda * lambda);
   }

   public static double getStandardDeviation(double gamma, double delta, double xi, double lambda) {
      return Math.sqrt(JohnsonSUDist.getVariance(gamma, delta, xi, lambda));
   }

   public void setParams(double gamma, double delta, double xi, double lambda) {
      setParams0(gamma, delta, xi, lambda);
   }
 
}