Urn models have a long history, starting with Laplace suggesting in 1786 that France's population be estimated by an urn-sampling scheme. They are conceptually relatively easy to understand, which also makes them easy to recognize and apply to a variety of real-world situations.
Urn with Black and White Balls
BernoulliDistribution — sampling of a single ball
BinomialDistribution — sampling with replacement until
balls are drawn
HypergeometricDistribution — sampling without replacement until
balls are drawn
GeometricDistribution — sampling with replacement until a white ball is drawn
NegativeBinomialDistribution — sampling with replacement until
white balls are drawn
WalleniusHypergeometricDistribution — biased sampling without replacement
FisherHypergeometricDistribution — biased sampling
at a time without replacement
BetaBinomialDistribution — sampling without replacement until
white balls are drawn
PoissonDistribution — sampling from urn with an infinite number of balls
Urn with Multiple Colored Balls
DiscreteUniformDistribution — sampling of a single ball
MultinomialDistribution — sampling with replacement until
n balls are drawn
MultivariateHypergeometricDistribution — sampling without replacement until
balls are drawn
NegativeMultinomialDistribution — sampling with replacement until
white balls are drawn
