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gptkb:standard_normal_distribution
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Φ(x)
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gptkb:von_Mises_distribution
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no closed form
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gptkb:Arcsin_distribution
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F(x) = (2/π) arcsin(√x) for x in [0,1]
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gptkb:Normal_Distribution
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Φ((x-μ)/σ)
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gptkb:Gumbel_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:Snedecor's_F-distribution
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involves regularized incomplete beta function
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gptkb:Pareto_distribution
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F(x; xm, α) = 1 - (xm/x)^α
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gptkb:univariate_normal_distribution
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Φ((x-μ)/σ)
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gptkb:Student's_t-distribution
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No simple closed form
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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:Inverse_chi-squared_distribution
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F(x; ν) = Γ(ν/2, 1/(2x))/Γ(ν/2)
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gptkb:Negative_binomial_distribution
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Sum of PMF up to k
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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:univariate_t-distribution
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expressed in terms of the incomplete beta 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:Pearson_Type_V
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CDF(x; a, b) = Γ(a, b/x) / Γ(a)
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gptkb:circular_normal_distribution
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no closed form
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gptkb:generalized_gamma_distribution
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expressed in terms of incomplete gamma function
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gptkb:exponential_distribution
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1 - exp(-lambda * x)
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