  Recently, the concept of cumulative residual entropy (CRE) has been studied
by many researchers in higher dimensions. In this article, we extend the
definition of (dynamic) cumulative past entropy (DCPE), a dual measure of
(dynamic) CRE, to bivariate setup and obtain some of its properties including
bounds. We also look into the problem of extending DCPE for conditionally
specified models. Several properties, including monotonicity, and bounds of
DCPE are obtained for conditional distributions. It is shown that the proposed
measure uniquely determines the distribution function. Moreover, we also
propose a stochastic order based on this measure.
