Discrete-stable distribution

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Discrete-stable distributions^[1] 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^[2] or even semantic networks.^[3]

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.^[4] It is the only discrete-stable distribution for which the mean and all higher-order moments are finite.^{[dubious – discuss]}