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gptkb:Chi-squared_distribution_(λ=0)
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γ(k/2, x/2)/Γ(k/2)
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gptkb:GEV_distribution
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closed form
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gptkb:chi_distribution
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P(x;k) = gamma(k/2, x^2/2) / Gamma(k/2)
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gptkb:Type_II_extreme_value_distribution
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F(x) = exp(-((x-m)/s)^-α) for x > m
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gptkb:Negative_Binomial_Distribution
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Regularized incomplete beta function
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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:t-distribution_(with_1_degree_of_freedom)
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(1/2) + (1/π) arctan(x)
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gptkb:circular_normal_distribution
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no closed form
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gptkb:Johnson_SU_distribution
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involves inverse hyperbolic sine
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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:Inverse_gamma_distribution
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Γ(α, β/x) / Γ(α)
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gptkb:normal_distribution
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(1/2)[1 + erf((x-μ)/(σ√2))]
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gptkb:beta_distribution
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regularized incomplete beta function
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gptkb:exponential_distribution_(when_k=1)
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F(x;λ) = 1 - e^{-λx} for x ≥ 0
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gptkb:Gumbel_distribution
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F(x) = exp(-exp(-(x-μ)/β))
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gptkb:Uniform_distribution_(when_alpha=1,_beta=1)
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x for x in [0,1]
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gptkb:geometric_distribution
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P(X ≤ k) = 1 - (1-p)^k
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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:Exponential_distribution
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1 - exp(-lambda * x)
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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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