Extropy: Dynamic cumulative past and residual inaccuracy measures with applications

Abstract

In comparison to probability density function based measures provided by extropy, the
cumulative distribution function based measures of cumulative residual and past extropies are
generally more stable. In this paper, we have extended the concept of cumulative extropy
to include both cumulative inaccuracy and dynamic versions, such as cumulative residual
inaccuracy and cumulative past inaccuracy. By using these measures, we have characterized
specific lifetime distributions and explored some generalized results. Additionally, we have
studied when these inaccuracy measures can uniquely identify the underlying distributions,
and we have also characterized 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.