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gptkb:gamma_distribution_(with_shape_n)
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incomplete gamma function
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gptkb:chi-squared_distribution
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γ(k/2, x/2)/Γ(k/2)
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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:Pareto_distribution
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F(x; xm, α) = 1 - (xm/x)^α
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gptkb:Johnson_SU_distribution
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involves inverse hyperbolic sine
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gptkb:Pearson_Type_V
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CDF(x; a, b) = Γ(a, b/x) / Γ(a)
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gptkb:triangular_distribution
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piecewise quadratic
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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:exponential_distribution
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1 - exp(-lambda * x)
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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:negative_binomial_distribution
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sum of PMFs up to k
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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:Negative_binomial_distribution
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Sum of PMF up to k
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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:circular_normal_distribution
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no closed form
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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:Standard_uniform_distribution
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F(x) = x for 0 ≤ x ≤ 1
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gptkb:Standard_normal_distribution
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Φ(x)
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gptkb:Normal_distribution_(standard_parameterization)
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Φ((x-μ)/σ)
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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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