Negative Binomial Distribution Sample Generator

This generator produces random samples from a negative binomial distribution defined as the number of failures \(X\) before the \(r\)th success, where the probability of success is \(1-p\) (and the failure probability is \(p\)).
Samples are generated by simulating Bernoulli trials until \(r\) successes occur.

* Enter the number of successes \( r \) (integer \(\ge1\)), the failure probability \( p \) (with \(0