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Cumulative residual entropy (CRE) is a new measure of uncertainty for continuous distributions which has been introduced by Rao et al. [27] and its discrete version has been defined by Baratpour and Bami [4]. The present paper addresses the question of extending the definition of CRE and its dynamic version to bivariate setup in discrete case and study its properties. We show that the proposed measure is invariance under increasing one-to-one transformation and has additive property. Also, a lower bound for discrete bivariate CRE based on Shannon entropy is obtained. Further more, we introduce scalar and vector bivariate dynamic CRE and their connections with well-known reliability measures such as the discrete bivariate mean residual life time. Finally, the bivariate version of the hazard rate, mean residual life and cumulative residual entropy are obtained for bivariate geometric distribution.

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