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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
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