Bivariate Extension of (Dynamic) Cumulative Past Entropy

TL;DR

This paper extends the concept of dynamic cumulative past entropy to bivariate distributions, exploring its properties, bounds, and applications in conditional models, and introduces a new stochastic order based on this measure.

Contribution

It introduces a bivariate extension of dynamic cumulative past entropy and studies its properties, bounds, and applications in conditional models, including a new stochastic order.

Findings

Proposed a bivariate extension of DCPE with unique distribution determination.

Derived properties and bounds for the extended measure.

Introduced a stochastic order based on the measure.

Abstract

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.