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-- To shuffle an array a of n elements (indices 0..n-1):
for i from 0 to n-2 do
     j <- random integer such that i <= j < n
     exchange a[i] and a[j]

$n = scalar(@aliased);
$a = $_ + rand @aliased - $_ # original code
...
   = random integer such that i <= j <= i+$n-i-1
   = random integer such that i <= j <= $n-1
   = random integer such that i <= j <  $n

for 0 .. $#aliased {
   $a = $_ + rand @aliased - $_;
...
   $aliased[ $_ ] = $aliased[ $a ],
   $aliased[ $a ] = $b
}

for i from 0 to n-1 do
   j <- random integer such that i <= j < n
   exchange a[i] and a[j]

#!/usr/bin/env perl

...
        my ($a, $b) = @_;
        return 100 - 100 * $a / $b
}

#!/usr/bin/env perl

...
        my ($a, $b) = @_;
        return 100 - 100 * $a / $b
}

#!/usr/bin/env perl

...
        my ($a, $b) = @_;
        return 100 - 100 * $a / $b
}

./random_walk_test.pl : done 10000000 trials with 10 bins, here is a s
+ummary:
./random_walk_test.pl : RandomWalk test : Math::Random::MT's rand() wi
+th mean %diff from expected to be 0.022 %
...

./transition_matrix_test.pl : best results for transition matrix test 
+: Perl's rand() with mean %diff from expected count to be 1.796 %
./transition_matrix_test.pl : end.