use strict;
    use warnings;
    use diagnostics;
    
    use Data::Dumper;
    use List::Util qw(sum);
    use Math::Random::MT qw(rand);
    
    
    open (F1,'>>event_times_new2.csv');
    open (F2,'>>lambda_star_new2.csv');
    
    my @event_times;
    my @net_event_times;
    my @immigrants;
    my @new_immigrants;
    my @s;
    my @d;
    my @u;
    my @v;
    my $lambda0;
    my $alpha;
    my $beta;
    my $result;
    my $sum;
    my $lambda_star;
    my $time;
    
    
    my $counterfails=0;
    my $num=1;
    
    
    $time=8000000;
    
    $lambda0=1.2;
    $alpha=0.8;
    $beta=0.9;
    
    #subroutine that computes intensity function
    
    sub lambda
    {
    my $t = $_[0];
    $sum=0;
    for (my $i=0; $i<@event_times; $i++)
    {
    
    $net_event_times[$i]=($t-$event_times[$i]);
    
    $immigrants[$i]=$alpha*exp(((-1)*$beta)*$net_event_times[$i]);
    
    }
    
    $sum= sum @immigrants;
    
    if ($immigrants[-1]==$alpha){
    $sum+=(-$alpha);
    }
    $result=$lambda0+$sum;
    
    return $result;
    }
    
    
    #ALGO it self
    
    
    for (my $i=0; $i<2; $i++)
    {
    if ($i==0){
    $lambda_star=$lambda0;
    $s[$i]=0;
    $d[$i]=0;
    
    $u[$i]=rand($num);
    $s[$i]=(-1)*(1/$lambda_star)*log($u[$i]);
    if ($s[$i]<$time){
    $event_times[$i]=$s[$i];
    
    print F1 "$event_times[$i]\n";
    print F2 "$lambda_star\n";
    }else{
    die
    }
    }else
    {
    my $valuelambda=lambda($event_times[(($i)-1)]);
    $lambda_star=$valuelambda+$alpha;
    
    START:
    $u[$i]=rand($num);
    $s[$i]=$s[(($i)-1)]+(-1)*(1/$lambda_star)*log($u[$i]);
    if ($s[$i]>$time){
    die
    }
    
    $d[$i]=rand($num) ;
    my $rejectionlambda=lambda($s[$i]);
    if ($d[$i]<($rejectionlambda/$lambda_star)){
    $event_times[$i]=$s[$i];
    
    print F1 "$event_times[$i]\n";
    print F2 "$lambda_star\n";
    }else{
    
    $counterfails+=1;
    $lambda_star=$rejectionlambda;
    goto START;
    }
    }
    }
    print F1 "The number of event-times that failed the A/R procedure is $counterfails\n";
    
    close F1;
    close F2;