[1] Conversely, a sub-Poissonian distribution has a smaller variance.
[2] The Poisson distribution is a result of a process where the time (or an equivalent measure) between events has an exponential distribution, representing a memoryless process.
In probability theory it is common to say a distribution, D, is a sub-distribution of another distribution E if D 's moment-generating function, is bounded by E 's up to a constant.
A distribution is strictly sub- if C ≤ 1.
From this definition a distribution, D, is sub-Poissonian if for all t > 0.