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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:discrete_uniform_distribution
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F(x) = (floor(x) - a + 1)/n for a ≤ x < b
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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:GEV_distribution
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closed form
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gptkb:inverse_gamma_distribution
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Γ(α, β/x) / Γ(α)
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gptkb:Log-gamma_distribution
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F(x; μ, θ, k) = γ(k, exp((x-μ)/θ))/Γ(k)
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gptkb:arcsine_distribution
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F(x) = (2/π) arcsin(√x) for x in [0,1]
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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:Fisher–Snedecor_distribution
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I_{d1 x/(d1 x + d2)}(d1/2, d2/2)
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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:Pareto_distribution
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F(x; xm, α) = 1 - (xm/x)^α
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gptkb:Log-normal_distribution
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F(x; μ, σ) = 0.5 + 0.5 erf[(ln x - μ)/(σ√2)]
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gptkb:Student's_t-distribution
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No simple closed form
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gptkb:Weibull_distribution_(with_shape_parameter_1)
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F(x) = 1 - exp(-x/λ) for x ≥ 0
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gptkb:Standard_normal_distribution
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Φ(x)
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gptkb:Inverse_gamma_distribution
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Γ(α, β/x) / Γ(α)
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gptkb:gamma_distribution_(with_shape_n)
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incomplete gamma function
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gptkb:generalized_Pareto_distribution
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F(x) = 1 - (1 + b(x-bc)/c)^{-1/b} for b
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gptkb:chi-squared_distribution_(with_2_degrees_of_freedom)
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F(x) = 1 - exp(-x/2) for x > 0
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gptkb:Arcsine_distribution_(when_alpha=beta=0.5)
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F(x) = (2/π) arcsin(√x) for 0 ≤ x ≤ 1
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