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gptkb:Gaussian_distribution
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Φ(x) = 0.5[1 + erf((x-μ)/(σ√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:exponential_distribution_(when_k=1)
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F(x;λ) = 1 - e^{-λx} for x ≥ 0
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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:Standard_Normal_Distribution
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Φ(x)
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gptkb:log-normal_distribution
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Φ((ln x - μ)/σ), x > 0
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gptkb:Rayleigh_distribution
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1 - exp(-x^2/(2σ^2)) for x ≥ 0
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gptkb:Snedecor's_F-distribution
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involves regularized incomplete beta function
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gptkb:normal_distribution
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(1/2)[1 + erf((x-μ)/(σ√2))]
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gptkb:Normal_distribution_(standard_parameterization)
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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:Gaussian_Distribution
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Φ((x-μ)/σ)
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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:Erlang_distribution
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1 - Σ_{n=0}^{k-1} e^{-λx} (λx)^n / n!
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gptkb:Inverse_chi-squared_distribution
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F(x; ν) = Γ(ν/2, 1/(2x))/Γ(ν/2)
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gptkb:univariate_normal_distribution
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Φ((x-μ)/σ)
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gptkb:standard_normal_distribution
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Φ(x)
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gptkb:Johnson_SB_distribution
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F(x) = Phi(gamma + delta * ln((x - xi)/(lambda + xi - x)))
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gptkb:Bernoulli_random_variable
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F(x) = 0 for x < 0, 1-p for 0 ≤ x < 1, 1 for x ≥ 1
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gptkb:beta_distribution
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regularized incomplete beta function
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