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