/**Calculates an approximation of the Poisson probability. * @param mean - lambda, the average number of occurrences * @param observed - the actual number of occurences observed * @return ln(Poisson probability) - the natural log of the Poisson probability. */public static double poissonProbabilityApproximation (double mean, int observed) {	double k = observed;	double a = k * Math.log(mean);	double b = -mean;	return a + b - factorialApproximation(k);}/**Srinivasa Ramanujan ln(n!) factorial estimation. * Good for larger values of n. * @return ln(n!) */public static double factorialApproximation(double n) {	if (n < 2.) return 0;	double a = n * Math.log(n) - n;	double b = Math.log(n * (1. + 4. * n * (1. + 2. * n))) / 6.;	return a + b + Math.log(Math.PI) / 2.;}