#!/usr/bin/perl

# poisson.pl by Konslow. Calculates the probability of observation k given an expected value lambda.
# Program uses stirling's approximation of the factorial to calculate the factorial of k.
# Tested on Ubuntu 14.04.
# Type ./poisson.pl lambda k where lambda and k are non-negative integers to use this program.
use strict; use warnings;

my ($lambda, $k) = @ARGV;

sub ln_fucktorial( $k ){
	(0.5 * log(2 * 3.14159265358979))
	+ ($k + 0.5) * log($k)
	- $k + 1 / (12 * $k)
	- 1 / (360 * ($k ** 3));
	}

sub k_fucktorial($k){
	2.71828 ** ln_fucktorial($k);
	}

my $i = 0;

if ($lambda <= 0) {
	print "lambda must be greater than 0!\n";
	$i++;
}
if ($lambda != int($lambda)) {
	print "lambda must be an integer!\n";
	$i++;
}
if ($k < 0) {
	print "k must be equal to or greater than 0!\n";
		$i++;
}
if ($k != int($k)) {
	print "k must be an integer!\n";
	$i++;
}
if ($i == 0) {
	print "\nPoisson's probability of k = $k occuring in lambda = $lambda is ", (($lambda ** $k) / k_fucktorial($k)) * (2.71828 ** (-$lambda)), "\n\n";
}