Negative Binomial Distribution

The Negative Binomial pdf is the probability of achieving 𝑟 failures before the 𝑥th success, with 𝑝 being the probability of a success.

Probability Density Function (PDF)

Cumulative Distribution Function (CDF)

where I_x(𝑎, 𝑏) is the regularized incomplete Beta function.

• Support 𝑥 ∈ {1,2,3, ...}
• Probability parameter, 𝑝: 0 ≤ 𝑝 ≤ 1
• Failure parameter, 𝑟: 𝑟 > 0