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Title: Understanding heavy tails in a bounded world or, is a truncated heavy tail heavy or not?
Authors: Chakrabarty, Arijit
Samorodnitsky, Gennady
Keywords: heavy tails
regular variation
Central Limit theorem
Hill estimator, consistency
Issue Date: 4-Aug-2009
Abstract: 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 had 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.
Appears in Collections:ORIE Technical Reports

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