ON GENERALIZED CUMULATIVE ENTROPIES

In the present paper, we introduce a generalization of the cumulative entropy proposed by Di Crescenzo and Longobardi [8]. This new notion is related to the lower records and the reversed relevation transform. Dynamic version of the newly proposed measure is considered. Several properties including the effect of linear transformations, a two-dimensional version, a normalized version, bounds, stochastic ordering, etc. are studied for the generalized cumulative entropy (GCE). Similar results are obtained for the dynamic GCE. Various relationships with other functions are derived. A class of distributions is introduced and several properties are studied. Finally, empirical GCE is proposed to estimate the newly proposed information measure.