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gptkbp:instanceOf
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gptkb:organization
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gptkbp:category
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gptkb:probability_theory
statistics
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gptkbp:convolution_of
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k independent exponential distributions with rate λ
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gptkbp:cumulativeDistributionFunction
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1 - Σ_{n=0}^{k-1} e^{-λx} (λx)^n / n!
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gptkbp:generalizes
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gptkb:gamma_distribution
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gptkbp:hasSpecialCase
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gamma distribution with integer shape parameter
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https://www.w3.org/2000/01/rdf-schema#label
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Erlang distribution
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gptkbp:isA
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continuous probability distribution
special case of gamma distribution
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gptkbp:kurtosis_excess
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6/k
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gptkbp:limiting_case
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gptkb:exponential_distribution_(when_k=1)
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gptkbp:meaning
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k/λ
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gptkbp:mode
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(k-1)/λ, for k > 1
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gptkbp:namedAfter
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gptkb:Agner_Krarup_Erlang
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gptkbp:parameter
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rate parameter λ (positive real number)
shape parameter k (positive integer)
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gptkbp:probability_density_function
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f(x; k, λ) = λ^k x^{k-1} e^{-λx} / (k-1)!
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gptkbp:relatedTo
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gptkb:Poisson_process
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gptkbp:skewness
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2/√k
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gptkbp:supports
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x ≥ 0
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gptkbp:used_in
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queueing theory
stochastic processes
telecommunications
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gptkbp:variant
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k/λ^2
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gptkbp:bfsParent
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gptkb:Gamma_distribution
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gptkbp:bfsLayer
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6
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