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gptkb:Inverse_gamma_distribution
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Γ(α, β/x) / Γ(α)
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gptkb:Standard_uniform_distribution
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F(x) = x for 0 ≤ x ≤ 1
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gptkb:Noncentral_t-distribution
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no closed form
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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:Noncentral_chi-squared_distribution
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No closed form
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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:Generalized_extreme_value_distribution
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F(x) = exp(- (1 + ξ((x-μ)/σ))^{-1/ξ})
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gptkb:Normal_distribution_(standard_parameterization)
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Φ((x-μ)/σ)
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gptkb:Weibull_distribution
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F(x; k, λ) = 1 - e^{-(x/λ)^k} for x ≥ 0
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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:Exponential_distribution
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1 - exp(-lambda * x)
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gptkb:Binomial_distribution
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Sum_{i=0}^k C(n, i) p^i (1-p)^{n-i}
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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:degenerate_distribution
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step function
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gptkb:exponential_distribution
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1 - exp(-lambda * x)
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gptkb:generalized_gamma_distribution
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expressed in terms of incomplete gamma function
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gptkb:Lorentz_distribution
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F(x; x0, γ) = (1/π) arctan((x - x0)/γ) + 1/2
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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:beta_distribution
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regularized incomplete beta function
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gptkb:Hypergeometric_distribution
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Sum of PMF from lower bound to k
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