  In this article two methods to distinguish between polynomial and exponential
tails are introduced. The methods are mainly based on the properties of the
residual coefficient of variation for the exponential and non-exponential
distributions. A graphical method, called CV-plot, shows departures from
exponentiality in the tails. It is, in fact, the empirical coefficient of
variation of the conditional excedance over a threshold. The plot is applied to
the daily log-returns of exchange rates of US dollar and Japan yen. New
statistics are introduced for testing the exponentiality of tails using
multiple thresholds. Some simulation studies present the critical points and
compare them with the corresponding asymptotic critical points. Moreover, the
powers of new statistics have been compared with the powers of some others
statistics for different sample size.
