In my limited testing Math::BigInt is two orders of magnitude faster than the next module I tried. At least it was on my crummy ole laptop. Just make sure to install the multicore module Math::BigInt::GMP as well which it uses to good advantage.

# Runtime:  0.15s user 0.02s system 41% cpu 0.418 total
use Math::BigInt lib => 'GMP';
my $b = Math::BigInt->new(35000);
print $b->bfac(),"\n";
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I guess you'll need to simplify the fraction in the first term before doing the calculations, as it is often the case in probability calculations. This makes the calculations much faster and more accurate.

I don't remember enough about multinomial distributions, but let me take a simple example: computing the number of permutations of 5 items in a population of 1000. The formula is: n!/(n-k)! or, in the example, 1000!/995! . You don't want to calculate 1000! (a number with 2570 digits) and then calculate 995! (only 2552 digits...) and then proceed with the division between the two huge numbers, whereas you really need only: 996 * 997 * 998 * 999 * 1000. In Perl, this could be expressed simply as follows:

my $result = 1;
$result *= $n-- while $k--;
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Some form of similar simplication should be possible in your case.

Otherwise, there are on the CPAN many probability and statistics modules, including some for calculating scores of different distributions.

Probably an entry point

http://adammonsen.com/post/173

Best regards
McA

UPDATE: You have to look at the comments on this page!

Do you really have to use perl for this? I mean, I love the language and everything, but there are much better ways to do this kind of thing. Like:

http://stat.ethz.ch/R-manual/R-patched/library/stats/html/Multinom.html

or: http://www.mathworks.com/help/stats/mnrnd.html

I don't know your situation, but I don't think mathematics and statistics is really perl's strong point. Maybe it makes sense to use something designed for that?

Of course Perl is per(l)fect for this task: I regularly use Perl to write R-scripts.

Or have a look at the following modules: R::YapRI, R::Writer or Statistics::R.

CountZero

A program should be light and agile, its subroutines connected like a string of pearls. The spirit and intent of the program should be retained throughout. There should be neither too little or too much, neither needless loops nor useless variables, neither lack of structure nor overwhelming rigidity." - The Tao of Programming, 4.1 - Geoffrey James

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