Open Access Open Access  Restricted Access Subscription or Fee Access

On Weighted Measures of Cumulative Entropy

Suchandan Kayal, Rajesh Moharana

Abstract


Motivated by the work of Di Crescenzo and Longobardi (2006), in this paper, we consider a shift-dependent information measure. We call it weighted cumulative entropy. Few basic properties including the effect of linear transformations, stochastic orders, bounds and inequalities are studied. Normalized version is proposed. Some connections of the measure under study to reliability theory are obtained. Bivariate version of the proposed measure is introduced. To include the effect of the current age to the weighted cumulative entropy, we consider a dynamic version and study similar results. Further, to enhance the study, we propose a non-parametric class based on the monotonicity property of the dynamic weighted cumulative entropy. We call it increasing dynamic weighted cumulative entropy (IDWCE) class. Several properties of the class are presented. Finally, we provide few applications of the proposed measures.

Keywords


Log-sum inequality, weighted mean inactivity time, reversed hazard rate, proportional reversed hazard model, non-singular transformation, IDWCE class.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.