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This paper considers a new generalization of cumulative residual extropy (CRJ) introduced by Jahanshahi et al. [On cumulative residual extropy. Probab Eng Inf Sci. 2019. DOI:10.1017/S0269964819000196], called weighted cumulative residual extropy (WCRJ). This paper studies some properties of WCRJ of continuous lifetime distributions. Several results including various bounds, inequalities, and effects of linear transformations are obtained. Conditional WCRJ and some of its properties are discussed. Related studies of survival analysis are covered. Also, we propose an empirical version of the WCRJ to estimate this measure of uncertainty. Based on the asymptotic distribution of empirical WCRJ, a new test statistic is given for testing the equality of two cumulative distribution functions. The power of the proposed test statistic is compared to other traditional and new competing approaches. Some simulations are carried out to show how this newly proposed method is more powerful than the others for moderate to large sample sizes.

On weighted cumulative residual extropy: characterization, estimation and testing