Bivariate Quantile-Based Entropy in Past Lifetime

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