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gptkbp:instanceOf
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Probability distribution
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gptkbp:application
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Bayesian statistics
Meteorology
Hydrology
Queuing models
Reliability engineering
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gptkbp:category
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Continuous probability distribution
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gptkbp:characteristic
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(1-iθt)^{-k}
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gptkbp:conjugatePriorFor
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gptkb:Poisson_distribution
gptkb:Exponential_distribution
Normal distribution (precision parameter)
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gptkbp:cumulativeDistributionFunction
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F(x;k,θ) = γ(k, x/θ) / Γ(k)
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gptkbp:entropy
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k + ln(θΓ(k)) + (1-k)ψ(k)
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gptkbp:firstDescribed
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gptkb:E._L._D._Gamma
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gptkbp:generalizes
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gptkb:Exponential_distribution
gptkb:Chi-squared_distribution
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gptkbp:hasSpecialCase
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gptkb:Pearson_Type_III_distribution
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https://www.w3.org/2000/01/rdf-schema#label
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Gamma distribution
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gptkbp:kurtosis
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6/k
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gptkbp:limitation
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Normal distribution (for large k)
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gptkbp:meaning
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kθ
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gptkbp:mode
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(k-1)θ, for k > 1
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gptkbp:momentGeneratingFunction
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(1-θt)^{-k}, for t < 1/θ
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gptkbp:namedAfter
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gptkb:Gamma_function
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gptkbp:parameter
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Rate parameter (θ or β)
Scale parameter (θ)
Shape parameter (k or α)
Shape-rate
Shape-scale
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gptkbp:pdf
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f(x;k,θ) = x^{k-1} e^{-x/θ} / (θ^k Γ(k)), x > 0
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gptkbp:relatedTo
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gptkb:Weibull_distribution
gptkb:Erlang_distribution
gptkb:Generalized_gamma_distribution
gptkb:Inverse_gamma_distribution
gptkb:Log-gamma_distribution
gptkb:Nakagami_distribution
gptkb:Poisson_distribution
gptkb:Beta_distribution
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gptkbp:skewness
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2/√k
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gptkbp:sumOf
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Independent exponential random variables
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gptkbp:supports
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x > 0
Real numbers greater than zero
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gptkbp:usedFor
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Modeling insurance claims
Modeling lifetimes of objects
Modeling rainfall amounts
Modeling waiting times
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gptkbp:usedIn
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gptkb:Probability_theory
Statistics
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gptkbp:variant
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kθ^2
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gptkbp:bfsParent
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gptkb:Pearson_distribution
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gptkbp:bfsLayer
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5
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