/* *
 * Title:        

 * Description:  

 * Copyright:    Copyright (c) 

 * Company:      

 * @author
 * @version 1.0
 */


package umontreal.iro.lecuyer.probdist;

/**
 * Extends the class {@link GammaDist} for the special case
 * of the Erlang distribution with
 * shape parameter k > 0 and scale parameter 
 * λ > 0.
 * This distribution is a special case of the gamma distribution
 * for which the shape parameter k = α is an integer.
 * 
 */
public class ErlangDist extends GammaDist {


   /**
    * Constructs a ErlangDist object with parameters
    *   k = k and λ = 1.
    * 
    */
   public ErlangDist (int k) {
      super (k);
   }


   /**
    * Constructs a ErlangDist object with parameters
    *   k = k  and λ = lambda.
    * 
    */
   public ErlangDist (int k, double lambda) {
      super (k, lambda);
   }


   /**
    * Computes the density function.
    * 
    */
   public static double density (int k, double lambda, double x) {
      return density ((double)k, lambda, x);
   }


   /**
    * Computes the distribution function using
    *    the gamma distribution function.
    * 
    */
   public static double cdf (int k, double lambda, int d, double x) {
      return cdf ((double)k, d, lambda*x);
   }


   /**
    * Computes the complementary distribution function.
    * 
    */
   public static double barF (int k, double lambda, int d, double x) {
      return barF ((double)k, d, lambda*x);
   }


   /**
    * Returns the inverse distribution function.
    * 
    */
   public static double inverseF (int k, double lambda, int d, double u) {
      return inverseF ((double)k, lambda, d, u);
   }


   /**
    * Estimates the parameters 
    * (k, λ) of the Erlang distribution
    *    using the maximum likelihood method, from the n observations
    *    x[i], 
    * i = 0, 1,…, n - 1. The estimates are returned in a two-element
    *     array, in regular order: [k, λ].
    * 
    * @param x the list of observations used to evaluate parameters
    * 
    *    @param n the number of observations used to evaluate parameters
    * 
    *    @return returns the parameters [hat(k), 
    * hat(λ)]
    * 
    */
   public static double[] getMLE (double[] x, int n) {
      double parameters[] = GammaDist.getMLE (x, n);
      parameters[0] = Math.round (parameters[0]);
      return parameters;
   }


   /**
    * Creates a new instance of an Erlang distribution with parameters k and
    *    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 ErlangDist getInstanceFromMLE (double[] x, int n) {
      double parameters[] = getMLE (x, n);
      return new ErlangDist ((int) parameters[0], parameters[1]);
   }


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


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

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


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

      return (Math.sqrt (k) / lambda);
   }


   /**
    * Returns the parameter k for this object.
    * 
    */
   public int getK() {
      return (int) getAlpha();
   }


   /**
    * Sets the parameters k and λ of the distribution for this
    *   object.  Non-static methods are computed with a rough target of
    *   d decimal digits of precision.
    * 
    */
   public void setParams (int k, double lambda, int d) {
      setParams (k, lambda, d);
   }


   /**
    * Return a table containing parameters of the current distribution.
    *    This table is put in regular order: [k, λ].
    * 
    * 
    */
   public double[] getParams () {
      return super.getParams();
   }


   public String toString () {
      return getClass().getSimpleName() + " : k = " + (int)super.getAlpha() + ", lambda = " + super.getLambda();
   }

}