/*
 * CompoundPoissonProcess.java
 *
 * Created on 3. Mai 2006, 16:26
 */

package WT;

/** Erzeugt eine Realisierung eines zusammengesetzten Poisson Prozesses (lambda, Exp(gamma)).
 *
 * @author  Stefanie Eckel
 */
public class CompoundPoissonProcess {
    
         
    public static void main(String[] args) {
 
        //Intensitaet
        double lambda = 0.2;

        //Intervalgrenze 
        int T = 100;  
        
        //Parameter der Exponential-Verteilung
        double gamma = 0.5;
        
        //Realisierung von N_t
        int n = PoissonProcess(lambda, T);
        
        //Summe ueber n exponential verteilte ZVen
        double sum = 0;
        for(int i=0;i<n;i++)
        {
            double u = java.lang.Math.random(); //generates a random number between 0 and 1
            double t = - Math.log(u)/gamma; //transforms u into an exponential distributed random variable with intensity gamma
               
            sum = sum + t;
        }
        System.out.println("Realisierung zusammengesetzter Poisson Prozess: "+sum);
    
    }
    
    
    /**Generates a realization of a Poisson process with intensity lambda in the interval [0,T]
     *
     *@param lambda the intensity 
     *@param T the interval border
     *
     *@return a realization of the Poisson process
     */
    public static int PoissonProcess(double lambda, int T)
    {
        double sum = 0;  
        int m = 0; 
        
        while(sum<T)
            {
                
                double u = java.lang.Math.random(); //generates a random number between 0 and 1
                double t = - Math.log(u)/lambda; //transforms u into an exponential distributed random variable with intensity lambda
                if(sum+t<T)
                {
                    sum = sum + t;
                    m++;
                }
                else
                    break;
            }
        return m;
        
    }
    
}