Negative Binomial Distribution
Models the number of failures before achieving a fixed number of successes. Common for overdispersed count data.
Probability Mass FunctionPMF = P(X = x)
Cumulative Distribution FunctionCDF = F(x)
Probability in an Interval
Compute the probability that X falls between two values. For discrete distributions, this is the sum of probabilities P(X = k) for all integers k from a to b.
P(a ≤ X ≤ b)
Quantiles (Inverse CDF)
Pick a probability p and read the corresponding quantile xₚ where F(xₚ) = p.
Quantile xₚ (where F(xₚ) = p)
In Negative Binomial Distribution, selected probability p: 0.9500 (95.00%)
Parameters
Adjust the parameters and (optionally) add up to 3 curves to compare different settings side‑by‑side.
0 curves shown
Estimating parameters from data
If you’re fitting this distribution to observed data, these are common plug‑in estimates you can start with.
Successes (r)
The target number of successes you want to achieve.
Probability (p)
Estimate from sample: p = r / (mean + r).