Definition:Negative Binomial Distribution/Terminology

Definition

There are two ways the negative binomial distribution is defined in the literature, both based on a Bernoulli Process:

Type $(1)$: the total number of Bernoulli trials before the $r$th success (or failure) has occurred

Type $(2)$: the total number of failures (or successes) before the $r$th success (or failure) has occurred.

Most sources give only one of these types of negative binomial distribution, defining it as either one or the other.

$\mathsf{Pr} \infty \mathsf{fWiki}$ is careful to define both types, and to distinguish between the two of them as appropriate.

Also see

• Results about negative binomial distributions can be found here.