The negative binomial is traditionally derived from a Poisson–gamma mixture model. However, the negative binomial may also be thought of as a member of the single parameter exponential family of distributions. This family of distributions admits a characterization known as generalized linear models (GLMs), which summarizes each member of the family. Most importantly, the characterization is applicable to the negative binomial. Such interpretation allows statisticians to apply to the negative binomial model the various goodness-of-fit tests and residual analyses that have been developed for GLMs.

Poisson regression is the standard method used to model count response data. However, the Poisson distribution assumes the equality of its mean and variance – a property that is rarely found in real data. Data that have greater variance than the mean are termed Poisson overdispersed, but are more commonly designated as simply overdispersed. Negative binomial regression is a standard method used to model overdispersed Poisson data.

When the negative binomial is used to model overdispersed Poisson count data, the distribution can be thought of as an extension to the Poisson model. Certainly, when the negative binomial is derived as a Poisson–gamma mixture, thinking of it in this way makes perfect sense. The original derivation of the negative binomial regression model stems from this manner of understanding it, and has continued to characterize the model to the present time.

As mentioned above, the negative binomial has recently been thought of as having an origin other than as a Poisson–gamma mixture.