Dynamical Effects of Truncated Tails
Stable distributions with heavy tails exhibit the Noah effect --- some dynamical measures are affected not only by the
correlated ordering of the data but also by the mere presence of more extreme values. This effect must always be considered
when dealing with heavy-tail data series. Another important consideration, however, is the possible truncation of such heavy tails.
Real data typically have some upper limit due to finite system size. This limit is statistically unlikely to be encountered by series
which are sufficiently short. Such series will display the dynamic hallmarks of the pure heavy-tail distribution. But the truncated
tails will look dynamically different for series which are long enough to excurse the truncation. Any effect caused by the extremities
will eventually (for long enough series) disappear if the extremities are truncated. A specific consequence is that the Noah effect
disappears on time scales beyond which the floods can get no larger.