Higher-order expansions of powered extremes of logarithmic general error distribution

In this paper, Let M_n denote the maximum of logarithmic general error distribution with parameter v ≥ 1. Higher-order expansions for distributions of powered extremes \(M_n^p\) $$M_n^p$$ are derived under an optimal choice of normalizing constants. It is shown that \(M_n^p\) $$M_n^p$$ , when v = 1, converges to the Fréchet extreme value distribution at the rate of 1/n, and if v > 1 then \(M_n^p\) $$M_n^p$$ converges to the Gumbel extreme value distribution at the rate of \({(\log \log n)^2}/{(\log n)^{1 - {1 \over v}}}\) .