Use of tail areas for testing goodness-of-fit

Characterizing a set of data as a random sample from a specified distribution is often a precursor to statistical inference or hypothesis testing involving the extremes of the distribution -precisely the regions of greatest uncertainty. It seems reasonable then to exploit as best we can our limited knowledge of this region. Toward this end we investigate here the areas in the tails of the distribution as determined by the extreme order statistics as a criterion for testing goodness-of-fit.