probabilityDensityFunction
30
triples
GPTKB property
Random triples
| Subject | Object |
|---|---|
| gptkb:Lorentzian_distribution | f(x; x0, γ) = [1/π] [γ / ((x - x0)^2 + γ^2)] |
| gptkb:circular_normal_distribution | f(θ; μ, κ) = [exp(κ cos(θ - μ))] / [2π I₀(κ)] |
| gptkb:Rayleigh_distribution | (x/σ^2) * exp(-x^2/(2σ^2)) for x ≥ 0 |
| gptkb:Pareto_distribution | f(x; xm, α) = α xm^α / x^(α+1) |
| gptkb:Arcsin_distribution | f(x) = 1 / (π√(x(1-x))) for x in (0,1) |
| gptkb:Extreme_Value_Type_I_distribution | f(x) = (1/β) exp(-(x-μ)/β) exp(-exp(-(x-μ)/β)) |
| gptkb:Log-normal_distribution | f(x; μ, σ) = (1/(xσ√(2π))) exp(-(ln x - μ)^2/(2σ^2)), x > 0 |
| gptkb:generalized_extreme_value_distribution | f(x) = (1/σ) [1 + ξ((x-μ)/σ)]^{-1/ξ-1} exp(-[1 + ξ((x-μ)/σ)]^{-1/ξ}) |
| gptkb:Gumbel_distribution | f(x) = (1/β) exp(-(z + exp(-z))) where z = (x - μ)/β |
| gptkb:Generalized_extreme_value_distribution | f(x) = (1/σ) exp(- (1 + ξ((x-μ)/σ))^{-1/ξ}) (1 + ξ((x-μ)/σ))^{-1-1/ξ} |
| gptkb:Inverse_gamma_distribution | (β^α / Γ(α)) x^(-α-1) exp(-β/x) |
| gptkb:GEV_distribution | closed form |
| gptkb:Johnson_SU_distribution | involves hyperbolic sine |
| gptkb:Dirichlet_distribution | f(x;α) = (1/B(α)) ∏ x_i^{α_i-1} |
| gptkb:Pearson_Type_I_distribution | f(x) = C (x-a)^{m-1} (b-x)^{n-1} |
| gptkb:multivariate_normal_distribution | f(x) = (1/((2π)^{k/2} |Σ|^{1/2})) exp(-1/2 (x-μ)^T Σ^{-1} (x-μ)) |
| gptkb:lognormal_distribution | f(x; μ, σ) = (1/(xσ√(2π))) exp(-(ln x - μ)^2/(2σ^2)), x > 0 |
| gptkb:double_exponential_distribution | f(x|μ,b) = (1/(2b)) * exp(-|x-μ|/b) |
| gptkb:inverse_Wishart_distribution | matrix-valued function |
| gptkb:log-normal_distribution | f(x; μ, σ) = (1/(xσ√(2π))) exp(-(ln x - μ)^2/(2σ^2)), x > 0 |