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gptkbp:instanceOf
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Probability distribution
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gptkbp:category
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gptkb:Exponential_family_distributions
Continuous probability distributions
Conjugate prior distributions
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gptkbp:conjugatePriorFor
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gptkb:Bernoulli_distribution
gptkb:Binomial_distribution
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gptkbp:continuity
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true
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gptkbp:cumulativeDistributionFunction
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regularized incomplete beta function
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gptkbp:entropy
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log B(alpha, beta) - (alpha-1)psi(alpha) - (beta-1)psi(beta) + (alpha+beta-2)psi(alpha+beta)
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gptkbp:firstDescribed
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19th century
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gptkbp:generalizes
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gptkb:Arcsine_distribution_(when_alpha=beta=0.5)
gptkb:Bernoulli_distribution_(as_a_prior)
gptkb:Uniform_distribution_(when_alpha=1,_beta=1)
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gptkbp:hasSpecialCase
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gptkb:Dirichlet_distribution
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https://www.w3.org/2000/01/rdf-schema#label
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Beta distribution
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gptkbp:kurtosis
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6*((alpha-beta)^2*(alpha+beta+1)-alpha*beta*(alpha+beta+2))/ (alpha*beta*(alpha+beta+2)*(alpha+beta+3))
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gptkbp:meaning
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alpha/(alpha+beta)
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gptkbp:mode
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(alpha-1)/(alpha+beta-2) (if alpha, beta > 1)
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gptkbp:namedAfter
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gptkb:Beta_function
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gptkbp:parameter
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alpha
beta
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gptkbp:pdf
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f(x; alpha, beta) = x^{alpha-1} (1-x)^{beta-1} / B(alpha, beta)
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gptkbp:relatedTo
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gptkb:Dirichlet_distribution
gptkb:Beta_function
gptkb:Bernoulli_distribution
gptkb:Binomial_distribution
gptkb:Gamma_distribution
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gptkbp:skewness
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(2*(beta-alpha)*sqrt(alpha+beta+1))/((alpha+beta+2)*sqrt(alpha*beta))
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gptkbp:supports
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interval [0, 1]
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gptkbp:usedFor
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modeling proportions
random variables in [0,1]
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gptkbp:usedIn
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Bayesian statistics
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gptkbp:variant
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(alpha*beta)/((alpha+beta)^2*(alpha+beta+1))
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gptkbp:bfsParent
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gptkb:F-distribution
gptkb:Pearson_distribution
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gptkbp:bfsLayer
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5
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