Extropy: Dynamic cumulative past and residual inaccuracy measures with applications

In comparison to PDF-based measures which provided by extropy, the CDF-based measures of cumulative residual and past extropies are generally more stable. In this paper, we extend the concept of cumulative extropy which includes both cumulative inaccuracy and dynamic versions, such as cumulative residual inaccuracy and cumulative past inaccuracy. By using these measures, we characterize specific lifetime distributions and explore some generalized results. Additionally, we find that these inaccuracy measures can uniquely identify the underlying distributions, and we also characterize a few specific lifetime distributions. Two non-parametric estimators for this measure are provided and their performances are compared via some simulation studies. Finally, we illustrate our method in a real data set.