一般误差分布下幂次顺序统计量的分布展开
Distributional expansions of powered order statistics from general error distribution
摘要：
设$\{X_{n}, n\ge 1\}$是一个具有共同广义误差分布$v>0$的独立随机变量序列，$M_{n,r}$表示$X_{1}, X_{2}, \cdots, X_{n}$的$r$第二大顺序统计量.利用不同的归一化常数，建立了归一化幂次顺序统计量$|M_{n,r}|^{p}$的分布展开式，并由此导出幂次顺序统计量收敛速度到极限的速度.本文推广了Hall关于正态序列幂极值的结果。
英文摘要：
Let $\{X_{n}, n\ge 1\}$ be a sequence of independent random variables with common 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 of normalized powered order statistics $|M_{n,r}|^{p}$ are established, from which the convergence rates of powered order statistics to their limits are derived. This paper generalized Hall's results on powered-extremes of normal sequence.
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