Title: Discrete dynamic cumulative residual entropy

Authors: Mohammad Khorashadizadeh; A.H. Rezaei Roknabadi; G.R. Mohtashami Borzadaran

Addresses: Department of Statistics, University of Birjand, Birjand, Iran ' Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran ' Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract: The concepts of cumulative residual entropy (CRE) and dynamic cumulative residual entropy (DCRE) were defined first in the continuous case by Rao et al. (2004), Rao (2005) and Asadi and Zohrevand (2007). In this paper, we define and study the discrete version of CRE and obtain a lower bound for it based on mean residual life (MRL) function. Also its relation with the class of new better (worse) than used in expectation and hazard rate is achieved. Furthermore the discrete version of normalised CRE (NCRE) is defined and illustrated by some examples. Also, the DCRE in the discrete case is introduced and a lower (an upper) bound is obtained. Finally, it is shown that the DCRE can characterise the distribution function and an example of real data is presented.

Keywords: Shannon entropy; cumulative residual entropy; DCRE; dynamic CRE; MRL; mean residual life; hazard rate.

DOI: 10.1504/IJRS.2016.081607

International Journal of Reliability and Safety, 2016 Vol.10 No.3, pp.210 - 226

Received: 03 Jan 2016
Accepted: 05 Nov 2016

Published online: 17 Jan 2017 *

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