Discrete-stable distribution

The 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 the continuous-stable distributions.

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

Both the 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 Poisson distribution which is a special case. It is the only discrete-stable distribution for which the mean and all higher-order moments are finite.