Discrete distributions come from a variety of backgrounds, but perhaps the most common relate back to the simple Bernoulli trial, which chooses between two outcomes, called success and failure here, whether you count the number of successes, the number of failures until first success, the number of failures until n ^th success, and so on. Other important origins are urn models with different sampling and replacement scenarios. Others are limit distributions of various kinds of processes.

Bernoulli-Related Distributions

BernoulliDistribution — distribution of an outcome of a Bernoulli trial

BinomialDistribution — the number of successes in Bernoulli trials

GeometricDistribution — the number of failures before the first success

NegativeBinomialDistribution — the number of failures before the ^th success

PascalDistribution — the number of trials for the ^th success

Urn-Related Distributions »

HypergeometricDistribution — sampling without replacement until balls are drawn

WalleniusHypergeometricDistribution  ▪  FisherHypergeometricDistribution  ▪  ...

Beta Mixture Distributions

BetaBinomialDistribution  ▪  BetaNegativeBinomialDistribution  ▪  WaringYuleDistribution

Poisson-Related Distribution

PoissonDistribution  ▪  SkellamDistribution

Uniform Distribution

DiscreteUniformDistribution

Power-Law Distributions

ZipfDistribution  ▪  LogSeriesDistribution  ▪  BenfordDistribution

Stopped-Sum Distribution

PolyaAeppliDistribution

Lagrangian Distribution

BorelTannerDistribution  ▪  PoissonConsulDistribution