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gptkb:Pareto_distribution
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F(x; xm, α) = 1 - (xm/x)^α
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gptkb:Generalized_extreme_value_distribution
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F(x) = exp(- (1 + ξ((x-μ)/σ))^{-1/ξ})
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gptkb:double_exponential_distribution
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F(x|μ,b) = 1 - 0.5 * exp(-(x-μ)/b) for x ≥ μ
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gptkb:Arcsin_distribution
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F(x) = (2/π) arcsin(√x) for x in [0,1]
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gptkb:Lévy_distribution
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F(x; μ, c) = erfc(sqrt(c / (2(x-μ)))), x > μ
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gptkb:Normal_Distribution
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Φ((x-μ)/σ)
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gptkb:uniform_distribution
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(x-a)/(b-a) for a ≤ x ≤ b
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gptkb:Gamma_distribution
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F(x;k,θ) = γ(k, x/θ) / Γ(k)
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gptkb:Exponential_distribution
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1 - exp(-lambda * x)
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gptkb:bernoulli_distribution
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0 for x<0, 1-p for 0≤x<1, 1 for x≥1
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gptkb:gamma_distribution_(with_shape_n)
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incomplete gamma function
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gptkb:Noncentral_chi-squared_distribution
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No closed form
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gptkb:Lorentzian_distribution
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F(x; x0, γ) = (1/π) arctan((x - x0)/γ) + 1/2
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gptkb:Noncentral_F-distribution
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no closed form
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gptkb:Extreme_Value_Type_I_distribution
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F(x) = exp(-exp(-(x-μ)/β))
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gptkb:t-distribution_(with_1_degree_of_freedom)
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(1/2) + (1/π) arctan(x)
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gptkb:chi-squared_distribution
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γ(k/2, x/2)/Γ(k/2)
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gptkb:Beta_distribution
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regularized incomplete beta function
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gptkb:double_exponential_distribution
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F(x|μ,b) = 0.5 * exp((x-μ)/b) for x < μ
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gptkb:Rayleigh_distribution
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1 - exp(-x^2/(2σ^2)) for x ≥ 0
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