/* *
 * Title:        

 * Description:  

 * Copyright:    Copyright (c) 

 * Company:      

 * @author
 * @version 1.0
 */

package umontreal.iro.lecuyer.probdist;

import  umontreal.iro.lecuyer.util.Num;

/**
 * Extends the class {@link ContinuousDistribution} for
 * the exponential distribution
 * with mean 1/λ where 
 * λ > 0.
 * Its density is
 * 

 * 
 * 

 * f (x) = λe-λx        for x >= 0,
 * 

 * its distribution function is
 * 

 * 
 * 

 * F(x) = 1 - e-λx,        for x >= 0,
 * 

 * and its inverse distribution function is
 * 

 * 
 * 

 * F-1(u) = - ln(1 - u)/λ,        for 0 < u < 1.
 * 

 * 
 */
public class ExponentialDist extends ContinuousDistribution {
   private double lambda;



   /**
    * Constructs an ExponentialDist object with parameter λ = 1.
    * 
    */
   public ExponentialDist() {
      setLambda (1.0);
   }


   /**
    * Constructs an ExponentialDist object with parameter λ =
    *   lambda.
    * 
    */
   public ExponentialDist (double lambda) {
      setLambda (lambda);
  }


   public double density (double x) {
      return density (lambda, x);
   }

   public double cdf (double x) {
      return cdf (lambda, x);
   }

   public double barF (double x) {
      return barF (lambda, x);
   }

   public double inverseF (double u) {
      return inverseF (lambda, u);
   }

   public double getMean() {
      return ExponentialDist.getMean (lambda);
   }

   public double getVariance() {
      return ExponentialDist.getVariance (lambda);
   }

   public double getStandardDeviation() {
      return ExponentialDist.getStandardDeviation (lambda);
   }

   /**
    * Computes the density function.
    * 
    */
   public static double density (double lambda, double x) {
      if (lambda <= 0)
         throw new IllegalArgumentException ("lambda <= 0");
      return x < 0 ? 0 : lambda*Math.exp (-lambda*x);
   }


   /**
    * Computes the  distribution function.
    * 
    */
   public static double cdf (double lambda, double x) {
      if (lambda <= 0)
         throw new IllegalArgumentException ("lambda <= 0");
      if (x <= 0.0)
         return 0.0;
      double y = lambda * x;
      if (y >= XBIG)
         return 1.0;
      return -Math.expm1 (-y);
   }


   /**
    * Computes the complementary distribution function.
    * 
    */
   public static double barF (double lambda, double x) {
      if (lambda <= 0)
         throw new IllegalArgumentException ("lambda <= 0");
      if (x <= 0.0)
         return 1.0;
      if (lambda*x >= XBIGM)
         return 0.0;
         return Math.exp (-lambda*x);
   }


   /**
    * Computes the inverse distribution function.
    * 
    */
   public static double inverseF (double lambda, double u) {
        if (lambda <= 0)
           throw new IllegalArgumentException ("lambda <= 0");
        if (u < 0.0 || u > 1.0)
            throw new IllegalArgumentException ("u not in [0,1]");
        if (u >= 1.0)
            return Double.POSITIVE_INFINITY;
        if (u <= 0.0)
            return 0.0;
        return -Math.log1p (-u)/lambda;
   }


   /**
    * Estimates the parameter λ of the exponential distribution
    *   using the maximum likelihood method, from the n observations
    *    x[i], 
    * i = 0, 1,…, n - 1. The estimate is returned in a one-element
    *     array, as element 0.
    * 
    * @param x the list of observations used to evaluate parameters
    * 
    *    @param n the number of observations used to evaluate parameters
    * 
    *    @return returns the parameter [
    * hat(λ)]
    * 
    */
   public static double[] getMLE (double[] x, int n)
   {
      if (n <= 0)
         throw new IllegalArgumentException ("n <= 0");

      double parameters[];
      double sum = 0.0;
      parameters = new double[1];
      for (int i = 0; i < n; i++)
         sum+= x[i];
      parameters[0] = (double) n / sum;

      return parameters;
   }


   /**
    * Creates a new instance of an exponential distribution with parameter
    *    λ estimated using
    *    the maximum likelihood method based on the n observations x[i],
    *    
    * i = 0, 1,…, n - 1.
    * 
    * @param x the list of observations to use to evaluate parameters
    * 
    *    @param n the number of observations to use to evaluate parameters
    * 
    * 
    */
   public static ExponentialDist getInstanceFromMLE (double[] x, int n) {
      double parameters[] = getMLE (x, n);
      return new ExponentialDist (parameters[0]);
   }


   /**
    * Computes and returns the mean, 
    * E[X] = 1/λ,
    *    of the exponential distribution with parameter λ.
    * 
    * @return the mean of the exponential distribution 
    * E[X] = 1/λ
    * 
    */
   public static double getMean (double lambda) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException ("lambda <= 0");

      return (1 / lambda);
   }


   /**
    * Computes and returns the variance, 
    * Var[X] = 1/λ2,
    *    of the exponential distribution with parameter λ.
    * 
    * @return the variance of the Exponential distribution 
    * Var[X] = 1/λ2
    * 
    */
   public static double getVariance (double lambda) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException ("lambda <= 0");

      return (1 / (lambda * lambda));
   }


   /**
    * Computes and returns the standard deviation of the
    *    exponential distribution with parameter λ.
    * 
    * @return the standard deviation of the exponential distribution
    * 
    */
   public static double getStandardDeviation (double lambda) {
      if (lambda <= 0.0)
         throw new IllegalArgumentException ("lambda <= 0");

      return (1 / lambda);
   }


   /**
    * Returns the value of λ for this object.
    * 
    */
   public double getLambda() {
      return lambda;
   }



   /**
    * Sets the value of λ for this object.
    * 
    */
   public void setLambda (double lambda) {
      if (lambda <= 0)
         throw new IllegalArgumentException ("lambda <= 0");
      this.lambda = lambda;
      supportA = 0.0;
   }


   /**
    * Return a table containing the parameters of the current distribution.
    * 
    * 
    */
   public double[] getParams () {
      double[] retour = {lambda};
      return retour;
   }


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

}