Urn Model Distributions

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

(RefLink[BernoulliDistribution, paclet:ref/BernoulliDistribution]) — sampling of a single ball

(RefLink[BinomialDistribution, paclet:ref/BinomialDistribution]) — sampling with replacement until n balls are drawn

(RefLink[HypergeometricDistribution, paclet:ref/HypergeometricDistribution]) — sampling without replacement until n balls are drawn

(RefLink[GeometricDistribution, paclet:ref/GeometricDistribution]) — sampling with replacement until a white ball is drawn

(RefLink[NegativeBinomialDistribution, paclet:ref/NegativeBinomialDistribution]) — sampling with replacement until n white balls are drawn

(RefLink[WalleniusHypergeometricDistribution, paclet:ref/WalleniusHypergeometricDistribution]) — biased sampling without replacement

(RefLink[FisherHypergeometricDistribution, paclet:ref/FisherHypergeometricDistribution]) — biased sampling n at a time without replacement

(RefLink[BetaBinomialDistribution, paclet:ref/BetaBinomialDistribution]) — number of white balls sampled from Polya's urn

(RefLink[PoissonDistribution, paclet:ref/PoissonDistribution]) — sampling from urn with an infinite number of balls

Urn with Multiple Colored Balls

(RefLink[DiscreteUniformDistribution, paclet:ref/DiscreteUniformDistribution]) — sampling of a single ball

(RefLink[MultinomialDistribution, paclet:ref/MultinomialDistribution]) — sampling with replacement until n balls are drawn

(RefLink[MultivariateHypergeometricDistribution, paclet:ref/MultivariateHypergeometricDistribution]) — sampling without replacement until n balls are drawn

(RefLink[NegativeMultinomialDistribution, paclet:ref/NegativeMultinomialDistribution]) — sampling with replacement until n white balls are drawn