Discrete-stable distribution

Discrete-stable distributions are a class of probability distributions with the property that the sum of several random variables from such a distribution under appropriate scaling is distributed according to the same family. They are the discrete analogue of continuous-stable distributions.

Discrete-stable distributions have been used in numerous fields, in particular in scale-free networks such as the internet and social networks or even semantic networks.

Both discrete and continuous classes of stable distribution have properties such as infinite divisibility, power law tails, and unimodality.

The most well-known discrete stable distribution is the special case of the Poisson distribution. It is the only discrete-stable distribution for which the mean and all higher-order moments are finite.