Bivariate Extension of Weighted Dynamic Survival Extropy and Its Quantile Approach

Abstract

This paper considers shift-dependent survival extropy in a bivariate setup and studies its properties. We also look into the problem of extending the same measure for conditionally specified models. It is shown that the proposed measure uniquely determines the distribution. Also, we established nonparametric estimators for the conditionally specified model, and the asymptotic properties of the proposed estimator are established under some regularity conditions. The effect of the proposed estimator is illustrated using simulated and real data sets. We have also proposed a quantile-based measure which uniquely determines the distribution. Also, we have obtained the real-life application of the proposed measure for a quantile function whose distribution function does not exist.