You are going to need the pass the file name to the get_statistics subroutine when you call it, which means you probably are going to need to save it in a globally accessible variable. You really should also be checking for definedness / existence of the file and success on open too. Also good practice to use lexical file handles and 3 argument opens. (Not critical but they can help avoid subtle bugs.)

my $current_file;
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$mw-> Button (-text =>'Get Statistics', -command => sub{ get_statistic
+s($current_file)});



sub open_file { 
    my $open = $mw->getOpenFile(
        -filetypes => $types_OPEN,
        -defaultextension => '.sff'
    );
    if (defined $open and -e $open){ 
        $te->Load( "$open");
        $current_file = $open;
}

sub get_statistics {

   # blah blah 

   my $fastaFile = shift;
   unless (defined $fastaFile){
        warn "No file name supplied.\n";
        return;
   }
   open my $FASTA, '<', $fastaFile or warn "Couldn't open file: $!\n";

   # blah blah

   while (<$FASTA>) {

   # blah blah
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 $mw-> Button (-text =>'Get Statistics', -command =>\&get_statistics($current_file));

The \&get_statistics($current_file) wouldn't work, as it would call the function right away (with an empty $current_file) at the time the button is set up, and set a reference to its return value as the button callback...  In other words, \&func is quite different from \&func(), with the former being a coderef to the function.

What you more likely want is

$mw-> Button (-text =>'Get Statistics', -command => sub { get_statisti
+cs($current_file) } );
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which would call the function with the current value of $current_file at the time the button is pressed.

Though, as the variable is global anyway, there's no real need to pass it, so you could also leave it at

    -command => \&get_statistics
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and access $current_file directly in the routine.

The OP's problem is primarily having made $open (i.e. the name of the selected file) scoped locally to the sub open_file, so it's not available outside of the routine.

system('perl.exe yourstatisticalroutine.pl inputfile.name >outputfile.
+name');
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Thank for your answer but unfortunately it still doesn't work. The code with your suggestions is:

# the firs button :
 $mw-> Button (-text =>'Open', -command =>\&open_file)->place(-x=>240,
+ -y=>35); 



#The seocnd button:
$mw-> Button (-text =>'Get Statistics',-command =>\&get_statistics)->p
+lace(-x=>320, -y=>35); 

# The sub open :
sub open_file {my $open = $mw->getOpenFile(
                               -filetypes => $types_OPEN,
                              -defaultextension => '.sff');
                                      $te->Load( "$open");}
if (defined $open and -e $open){ 
        $te->Load( "$open");
        $current_file = $open;
}



# the sub get statistic:

sub get_statistics {my $stat = Statistics::Descriptive::Full->new();
my (%distrib);
my @bins = qw/18 19 20 21 22 23 24 25 26 27 28/;
my $fastaFile = shift;
   unless (defined $fastaFile){
        warn "No file name supplied.\n";
        return;
   }
   open my $FASTA, '<', $fastaFile or warn "Couldn't open file: $!\n";
my $junkFirstOne = <FASTA>;

while (<$FASTA>) {chomp;
    my ($def,@seqlines) = split /\n/, $_;
    my $seq = join '', @seqlines;
    $stat->add_data(length($seq));}


%distrib = $stat->frequency_distribution(\@bins);

print "Total reads:\t" . $stat->count() . "\n";
print "Total nt:\t" . $stat->sum() . "\n";
print "Mean length:\t" . $stat->mean() . "\n";
print "Median length:\t" . $stat->median() . "\n";
print "Mode length:\t" . $stat->mode() . "\n";
print "Max length:\t" . $stat->max() . "\n";
print "Min length:\t" . $stat->min() . "\n";
print "Length\t# Seqs\n";
foreach (sort {$a <=> $b} keys %distrib) {
    print "$_\t$distrib{$_}\n";
}};

# The scrolled window:
$te = $mw->Scrolled( q/TextUndo/, -scrollbars => 'se', -background => 
+'white', -font => [-family =>'arial',-size => '12',-weight=> 'bold'],
+-wrap => 'none',)->pack(-anchor =>'n',-side=>'right',-fill=>'none');
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It say me (after load the $open file in the scrolled window and push the get_statistic button) : "No file name supplied". Where i need to correct the script to make it works ? Thanks