A shift-dependent generalized cumulative entropy of order n

Recently, a shift-independent information measure known as generalized cumulative entropy of order n (GCE_n) was proposed by Kayal (2016 Kayal, S. 2016. On generalized cumulative entropies. Probability in Engineering and Informational Sciences 30:640–62. Google Scholar]). In this communication, we propose a shift-dependent version of GCE_n. Various properties including the effect of transformations, bounds etc. have been discussed. Several relationships of the shift-dependent GCE_n with some well-known reliability measures are studied. Few characterization results are obtained. We derive an estimator for the proposed measure via empirical distribution function approach. Large sample properties of the estimator are studied when independent observations are taken from a Weibull distribution.