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We discuss in this paper a possibility of constructing a whole class ofasymptotic distribution-free tests for testing regularly varying taildistributions. The idea is that we treat the tails of distributions as membersof a parametric family and using MLE to estimate the exponent. No matter whatthe exponent's estimator is, we are able to transform the whole class into aspecific distribution with a prefix exponent so that we are free from choosingany functional of the tail empirical process as a distribution-free teststatistic. The asymptotic behavior of some new tests, as examples from thewhole class of new tests, are demonstrated as well.

Distribution free goodness of fit tests for regularly varying tail distributions