In mathematics, a super-Poissonian distribution is a probability distribution that has a larger variance than a Poisson distribution with the same mean. Conversely, a sub-Poissonian distribution has a smaller variance.
An example of super-Poissonian distribution is negative binomial distribution.
The Poisson distribution is a result of a process where the time (or an equivalent measure) between events has an Exponential distribution, representing a memoriless process.
References
Super-Poissonian distribution Wikipedia(Text) CC BY-SA