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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: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: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:normal_distribution
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(1/2)[1 + erf((x-μ)/(σ√2))]
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gptkb:Hypergeometric_distribution
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Sum of PMF from lower bound to k
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gptkb:standard_normal_distribution
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Φ(x)
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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:Negative_Binomial_Distribution
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Regularized incomplete beta function
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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:generalized_Pareto_distribution
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F(x) = 1 - (1 + b(x-bc)/c)^{-1/b} for b
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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:Negative_binomial_distribution
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Sum of PMF up to k
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gptkb:univariate_t-distribution
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expressed in terms of the incomplete beta function
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gptkb:geometric_distribution
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P(X ≤ k) = 1 - (1-p)^k
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gptkb:negative_binomial_distribution
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sum of PMFs up to k
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gptkb:exponential_distribution
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1 - exp(-lambda * x)
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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: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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gptkb:univariate_normal_distribution
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Φ((x-μ)/σ)
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