X  ∼  F ( x ) | Support | i | α | \(\boldsymbol {b_{n} }\) | \(\boldsymbol {c_{n}}\) |
---|---|---|---|---|---|
exponential | (0,∞) | 1 | \(n_{1} \) | 1 | |
logistic | \(\mathbb{R} \) | 1 | \(n_{1} \) | 1 | |
normal | \(\mathbb{R} \) | 1 | \(B_{n}\) | \(( 2n_{1} )^{1/2}\) | |
log-normal | (0,∞) | 1 | \(B_{n}^{\prime}\) | \(( 2n_{1} )^{-1/2} B_{n}^{\prime}\) | |
1 − exp(1/x) | (−∞,1) | 1 | \(-n_{1}^{-1} \) | \(n_{1}^{-2}\) | |
Pareto \(1-(a/x)^{\alpha}\) | (a,∞) | 2 | α | 0 | \(an^{1/ \alpha}\) |
Cauchy | \(\mathbb{R}\) | 2 | 1 | 0 | \(n^{-1}\) |
uniform | (0,1) | 3 | 1 | 1 | \(n^{-1}\) |
\(1 - (x_{0} - x )^{\alpha} \) | \((x_{0}-1, x_{0} )\) | 3 | α | \(x_{0}\) | \(n^{-1/\alpha}\) |
\(\{ 1-\exp(-x) \} / \{ 1 - \exp (-x_{0} ) \}\) | \((0,x_{0} )\) | 3 | 1 | \(x_{0}\) | \(\{ \exp (x_{0} ) - 1 \} / n\) |
\(G_{1}\) | \(\mathbb{R}\) | 1 | 1 | 1 | |
\(G_{2}\) | (0,∞) | 2 | α | 0 | \(n^{1/ \alpha}\) |
\(G_{3}\) | (−∞,0) | 3 | α | 0 | \(n^{-1/\alpha}\) |