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gptkb:Pearson_Type_X_distribution
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regularized incomplete beta function
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gptkb:uniform_distribution
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(x-a)/(b-a) for a ≤ x ≤ b
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gptkb:geometric_distribution
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P(X ≤ k) = 1 - (1-p)^k
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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:Negative_binomial_distribution
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Sum of PMF up to k
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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:Extreme_Value_Type_I_distribution
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F(x) = exp(-exp(-(x-μ)/β))
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gptkb:Chi-squared_distribution
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P(x; k) = γ(k/2, x/2)/Γ(k/2)
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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:Normal_Distribution
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Φ((x-μ)/σ)
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gptkb:Bernoulli_distribution
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0 for x<0, 1-p for 0≤x<1, 1 for x≥1
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gptkb:Noncentral_t-distribution
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no closed form
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gptkb:Snedecor's_F-distribution
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involves regularized incomplete beta function
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gptkb:GEV_distribution
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closed form
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gptkb:standard_normal_distribution
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Φ(x)
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gptkb:Fréchet_distribution
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F(x; α, s, m) = exp(-((x-m)/s)^(-α)) for x > m
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gptkb:normal_distribution
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(1/2)[1 + erf((x-μ)/(σ√2))]
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gptkb:Exponential_distribution
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1 - exp(-lambda * x)
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gptkb:Noncentral_F-distribution
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no closed form
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gptkb:univariate_t-distribution
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expressed in terms of the incomplete beta function
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