Zusammenfassung
We address the important question of the extent to which random variables and
vectors with truncated power tails retain the characteristic features of random
variables and vectors with power tails. We define two truncation regimes, soft
truncation regime and hard truncation regime, and show that, in the soft
truncation regime, truncated power tails behave, in important respects, as if
no truncation took place. On the other hand, in the hard truncation regime much
of "heavy tailedness" is lost. We show how to estimate consistently the tail
exponent when the tails are truncated, and suggest statistical tests to decide
on whether the truncation is soft or hard. Finally, we apply our methods to two
recent data sets arising from computer networks.
Nutzer