Distributional expansions of powered order statistics from general error distribution
Abstract
Let \Xn, n 1\ be a sequence of independent random variables with common general error distribution GED(v) with shape parameter v>0, and let Mn,r denote the rth largest order statistics of X1, X2, ·s, Xn. With different normalizing constants the distributional expansions of normalized powered order statistics |Mn,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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