  In the recent information-theoretic literature, the concept of extropy has
been studied for order statistics. In the present communication we consider a
cumulative analogue of extropy in the same vein of cumulative residual (past)
entropy and study it in context with extreme order statistics. A dynamic
version of cumulative residual (past) extropy for smallest (largest) order
statistic is also studied here. It is shown that the proposed measures (and
their dynamic versions) of extreme order statistics determine the distribution
uniquely. Some characterizations of the generalized Pareto and power
distributions, which are commonly used in reliability modeling, are given.
