Negative Binomial Distribution Median Calculator

For a negative binomial distribution defined as the number of failures \(X\) before the \(r\)th success with failure probability \(p\), the CDF is: $$ F(X \le x)=\sum_{i=0}^{x} \binom{i+r-1}{i}(1-p)^r p^i, \quad x=0,1,2,\dots $$

The median is defined as the smallest integer \(m\) such that \(F(m)\ge0.5\).

* Enter the failure count range parameter: the number of successes \(r\) (integer \(\ge1\)) and the failure probability \( p \) (with \(0