  We consider the fitting of heavy tailed data and distribution with a special
attention to distributions with a non--standard shape in the "body" of the
distribution. To this end we consider a dense class of heavy tailed
distributions introduced recently, employing an EM algorithm for the the
maximum likelihood estimates of its parameters. We present methods for fitting
to observed data, histograms, censored data, as well as to theoretical
distributions. Numerical examples are provided with simulated data and a
benchmark reinsurance dataset. We empirically demonstrate that our model can
provide excellent fits to heavy--tailed data/distributions with minimal
assumptions
