Bivariate Dynamic Weighted Survival Entropy of Order 𝛼

Abstract

Abstract Recently, G. Rajesh, E. I. Abdul-Sathar and S. Nair Rohini [G. Rajesh, E. I. Abdul-Sathar and S. Nair Rohini, On dynamic weighted survival entropy of order α, Comm. Statist. Theory Methods 46 2017, 5, 2139–2150] proposed a measure of uncertainty based on the survival function called weighted survival entropy of order α. They have also introduced the dynamic form of a measure called dynamic weighted survival entropy of order α and studied various properties in the context of reliability modeling. In this paper, we extend these measures into the bivariate setup and study its properties. We also look into the problem of extending the same measure for conditionally specified models. Empirical and non-parametric estimators are suggested for the proposed measure using the conditionally specified model, and the effect of the proposed estimators is illustrated using simulated and real data sets.