The Poisson distribution, the stuttering Poisson distribution, the negative binomial distribution, and the Gamma distribution are examples of infinitely divisible distributions — as are the normal distribution, Cauchy distribution and all other members of the stable distribution family. The skew-normal distribution is an example of a non-infinitely divisible distribution. (See Domínguez-Molina and Rocha-Arteaga (2007).)
