Bivariate Quantile-Based Entropy in Past Lifetime

Eventhough considerable research is now available on the study of entropy using quantile function, a bivariate extension same has not been considered so far. In present study, we propose version vector-valued differential function in past life and its various properties. We prove characterization theorems for some well-known lifetime models. It shown that proposed measure uniquely determines function. also reliability properties quantile-based examine usefulness through real data set.