Further results on the generalized cumulative entropy

Recently, a new concept of entropy called generalized cumulative entropy of order n was introduced and studied in the literature. It is related to the lower record values of a sequence of independent and identically distributed random variables and with the concept of reversed relevation transform. In this paper, we provide some further results for the generalized cumulative entropy such as stochastic orders, bounds and characterization results. Moreover, some characterization results are derived for the dynamic generalized cumulative entropy. Finally, it is shown that the empirical generalized cumulative entropy of an exponential distribution converges to normal distribution.