  The so-called partition function is a sample moment statistic based on blocks
of data and it is often used in the context of multifractal processes.
  It will be shown that its behaviour is strongly influenced by the tail of the
distribution underlying the data either in i.i.d. and weakly dependent cases.
  These results will be exploited to develop graphical and estimation methods
for the tail index of a distribution. The performance of the tools proposed is
analyzed and compared with other methods by means of simulations and examples.
