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This paper lists the continuous limit distributions for central order statistics normalized by power transformations, and describes their domains of attraction. One may argue that power transformations are the natural normalizations to use if one wants to study the asymptotic behaviour of central order statistics. Power transformations preserve the origin, which may be assumed to be the quantile to...
For order statistics there is a deceptively simple link between affine and power norming, using exponential transforms. This link does not tell the whole story about limit distributions. The exponential transforms and yield limit variables which are either positive or negative. Under power norming there exist discrete limit distributions for maxima. The corresponding limit...
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