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Just a note

Arranged in order of their skewness, here are some models which produce overdispersed counts.

  • Thomas double Poisson:
    arises from a Poisson distributed population, the reproductive success of which is Poisson distributed, and the progeny are subject to random but limited dispersal.
  • Neyman contagious type A:
    arises from a Poisson distributed population, each member of which gives rise to equal-sized groups randomly distributed around the original members.
  • Polya-Aeppli:
    randomly distributed colonies where the number of individuals per colony is geometrically distributed.
  • Negative binomial:
    among many other mechanisms - a continuously reinvading Thomas double Poisson. Or Poisson distributed samples, with mean λ, which is gamma-distributed.
  • Poisson lognormal (or discrete lognormal):
    Samples are Poisson distributed, with mean λ, which is lognormally-distributed.