/* *
 * Title:        

 * Description:  

 * Copyright:    Copyright (c) 

 * Company:      

 * @author
 * @version 1.0
 */


package umontreal.iro.lecuyer.probdist;


/**
 * Extends the class {@link DiscreteDistributionInt} for the Bernoulli
 * distribution with parameter p, where 
 * 0 <= p <= 1.
 * Its mass function is given by
 * 

 * 
 * 

 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
f (x) =
1 - p,
         if x = 0;
f (x) =
p,
         if x = 1;
f (x) =
0,
         otherwise. 
 * 

 * Its distribution function is
 * 

 * 
 * 

 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
 * 
F(x) =
0,
         if x < 0;
F(x) =
1 - p,
         if 0 <= x < 1;
F(x) =
1,
         if x >= 1.
 * 

 * 
 */
public class BernoulliDist extends DiscreteDistributionInt {
   private double p;
   private double q;



   /**
    * Creates a Bernoulli distribution object.
    * 
    */
   public BernoulliDist (double p) {
      if (p < 0.0 || p > 1.0)
         throw new IllegalArgumentException ("p not in [0,1]");
      this.p = p;
      q = 1 - p;
      supportA = 0;
      supportB = 1;
   }

   public double prob (int x) {
      if (1 == x) return p;
      if (0 == x) return q;
      return 0.0;
   }

   public double cdf (int x) {
      if (x < 0) return 0.0;
      if (x < 1) return q;
      return 1.0;
   }

   public double barF (int x) {
      if (x > 1) return 0.0;
      if (x > 0) return p;
      return 1.0;
   }

   public int inverseFInt (double u) {
      if (u < 0.0 || u > 1.0)
         throw new IllegalArgumentException ("u not in [0,1]");
      if (u > q) return 1;
      return 0;
   }

   public double getMean() {
      return BernoulliDist.getMean (p);
   }

   public double getVariance() {
      return BernoulliDist.getVariance (p);
   }

   public double getStandardDeviation() {
      return BernoulliDist.getStandardDeviation (p);
   }



   /**
    * Returns the Bernoulli probability f (x) with parameter p
    * (see eq.).
    * 
    */
   public static double prob (double p, int x) {
      if (p < 0.0 || p > 1.0)
         throw new IllegalArgumentException ("p not in [0,1]");
      if (1 == x) return p;
      if (0 == x) return 1.0 - p;
      return 0.0;
   }


   /**
    * Returns the Bernoulli distribution function F(x)
    *  with parameter p (see eq.).
    * 
    */
   public static double cdf (double p, int x) {
      if (p < 0.0 | p > 1.0)
         throw new IllegalArgumentException ("p not in [0,1]");
      if (x < 0) return 0.0;
      if (x < 1) return 1.0 - p;
      return 1.0;
   }


   /**
    * Returns the complementary Bernoulli distribution
    *   function 
    * bar(F)(x) = P[X >= x] with parameter p.
    * 
    */
   public static double barF (double p, int x) {
      if (p < 0.0 | p > 1.0)
         throw new IllegalArgumentException ("p not in [0,1]");
      if (x > 1) return 0.0;
      if (x > 0) return p;
      return 1.0;
   }


   /**
    * Returns the inverse of the Bernoulli distribution function
    *  with parameter p at u.
    * 
    */
   public static int inverseF (double p, double u)  {
      if (p < 0.0 | p > 1.0)
         throw new IllegalArgumentException ("p not in [0,1]");
      if (u < 0.0 || u > 1.0)
         throw new IllegalArgumentException ("u not in [0,1]");
      if (u > 1.0 - p) return 1;
      return 0;
    }


   /**
    * Estimates the parameters p of the Bernoulli distribution
    *    using the maximum likelihood method, from the m observations
    *    x[i], 
    * i = 0, 1,…, m - 1. The estimate is returned in a one-element
    *     array: [p].
    * 
    * @param x the list of observations used to evaluate parameters
    * 
    *    @param m the number of observations used to evaluate parameters
    * 
    *    @return returns the parameter [hat(p)]
    * 
    */
   public static double[] getMLE (int[] x, int m) {
      if (m < 2)
         throw new UnsupportedOperationException(" m < 2");

      // compute the empirical mean
      double sum = 0.0;
      for (int i = 0; i < m; i++)
         sum += x[i];
      sum /= (double) m;

      double param[] = new double[1];
      param[0] = sum;
      return param;
   }


   /**
    * Creates a new instance of a Bernoulli distribution with parameter
    *    p estimated using the maximum likelihood method, from
    *    the m observations x[i],  
    * i = 0, 1,…, m - 1.
    * 
    * @param x the list of observations to use to estimate the parameters
    * 
    *    @param m the number of observations to use to estimate the parameters
    * 
    * 
    */
   public static BernoulliDist getInstanceFromMLE (int[] x, int m) {
      double param[] = new double[1];
      param = getMLE (x, m);
      return new BernoulliDist (param[0]);
   }


   /**
    * Returns the mean E[X] = p of the Bernoulli distribution with
    *    parameter p.
    * 
    * @return the mean of the Bernoulli distribution E[X] = np
    * 
    */
   public static double getMean (double p) {
      if (p < 0.0 || p > 1.0)
         throw new IllegalArgumentException ("p not in [0, 1]");

      return (p);
   }


   /**
    * Computes the variance 
    * Var[X] = p(1 - p) of the Bernoulli
    *    distribution with parameter p.
    * 
    * @return the variance of the Bernoulli distribution
    * 
    */
   public static double getVariance (double p) {
      if (p < 0.0 || p > 1.0)
         throw new IllegalArgumentException ("p not in [0, 1]");
      return (p * (1.0 - p));
   }


   /**
    * Computes the standard deviation of the Bernoulli distribution
    *    with parameter p.
    * 
    * @return the standard deviation of the Bernoulli distribution
    * 
    */
   public static double getStandardDeviation (double p) {
      return Math.sqrt (BernoulliDist.getVariance (p));
   }


   /**
    * Returns the parameter p of this object.
    * 
    */
   public double getP() {
      return p;
   }


   /**
    * Returns an array that contains the parameter p of the current
    *    distribution: [p].
    * 
    */
   public double[] getParams () {
      double[] retour = {p};
      return retour;
   }


   /**
    * Resets the parameter to this new value.
    * 
    * 
    */
   public void setParams (double p) {
      this.p = p;
      q = 1 - p;
   }


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

}