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The Negative Binomial Distribution

\[ P(k \mid r, p) = \binom{k + r - 1}{k} p^{r} (1 - p)^{k} \]

The negative binomial distribution models the number of failures (k) before achieving a fixed number of successes (r) in a sequence of independent Bernoulli trials with success probability p.

If you're dealing with negative binomial processes and have observed data, you can use this calculator to compute the posterior probability distribution of p for the process.