Beta-binomial distribution

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:organization
gptkbp:application	ecology genetics quality control modeling overdispersion in count data
gptkbp:category	discrete distribution
gptkbp:conjugatePriorFor	binomial likelihood
gptkbp:describes	number of successes in n Bernoulli trials with random probability
gptkbp:generalizes	gptkb:binomial_distribution
gptkbp:hasSpecialCase	compound distribution
https://www.w3.org/2000/01/rdf-schema#label	Beta-binomial distribution
gptkbp:limitation	binomial distribution (as α, β → ∞)
gptkbp:meaning	nα/(α+β)
gptkbp:namedAfter	gptkb:beta_distribution gptkb:binomial_distribution
gptkbp:overdispersedRelativeTo	gptkb:binomial_distribution
gptkbp:parameter	α n β shape parameters (α, β)
gptkbp:probabilityMassFunction	P(X = k) = (n choose k) * B(k+α, n−k+β) / B(α, β)
gptkbp:relatedTo	gptkb:beta_distribution gptkb:binomial_distribution
gptkbp:supports	k = 0, 1, ..., n
gptkbp:usedIn	Bayesian statistics
gptkbp:variant	nαβ(α+β+n)/(α+β)^2(α+β+1)
gptkbp:bfsParent	gptkb:Polya_urn_scheme
gptkbp:bfsLayer	8