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.

ReferenceReference

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

New to Mathematica? Find your learning path »
Have a question? Ask support »