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gptkbp:instanceOf
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gptkb:organization
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gptkbp:application
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material strength analysis
modeling lifetimes of objects
wind speed analysis
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gptkbp:category
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continuous probability distribution
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gptkbp:cumulativeDistributionFunction
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F(x; k, λ) = 1 - e^{-(x/λ)^k} for x ≥ 0
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gptkbp:field
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gptkb:probability_theory
statistics
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gptkbp:firstDescribed
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1939
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gptkbp:hasSpecialCase
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gptkb:exponential_distribution_(when_k=1)
gptkb:generalized_extreme_value_distribution
Rayleigh distribution (when k=2)
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https://www.w3.org/2000/01/rdf-schema#label
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Weibull distribution
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gptkbp:kurtosis
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depends on shape parameter k
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gptkbp:meaning
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λ Γ(1 + 1/k)
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gptkbp:namedAfter
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gptkb:Waloddi_Weibull
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gptkbp:parameter
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location parameter (optional, θ)
scale parameter (λ)
shape parameter (k)
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gptkbp:pdf
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f(x; k, λ) = (k/λ) (x/λ)^{k-1} e^{-(x/λ)^k} for x ≥ 0
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gptkbp:relatedTo
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gptkb:Gumbel_distribution
gptkb:gamma_distribution
gptkb:log-normal_distribution
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gptkbp:skewness
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depends on shape parameter k
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gptkbp:supports
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x ≥ 0
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gptkbp:usedIn
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hydrology
survival analysis
weather forecasting
reliability engineering
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gptkbp:variant
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λ^2 [Γ(1 + 2/k) - (Γ(1 + 1/k))^2]
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gptkbp:bfsParent
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gptkb:exponential_distribution
gptkb:log-normal_distribution
gptkb:Fisher–Tippett_distribution
gptkb:Gamma_distribution
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gptkbp:bfsLayer
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6
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