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Let $\{X_{n}, n\ge 1\}$ be a sequence of independent random variables withcommon general error distribution $GED(v)$ with shape parameter $v>0$, and let$M_{n,r}$ denote the $r$th largest order statistics of $X_{1}, X_{2}, \cdots,X_{n}$. With different normalizing constants the distributional expansions ofnormalized powered order statistics $|M_{n,r}|^{p}$ are established, from whichthe convergence rates of powered order statistics to their limits are derived.This paper generalized Hall's results on powered-extremes of normal sequence.

Distributional expansions of powered order statistics from general error distribution