Copula-Based Modeling of Fractional Inaccuracy: A Unified Framework

TL;DR

This paper introduces new multivariate copula-based measures of fractional inaccuracy, providing a unified framework that captures dependence structures and extends traditional inaccuracy concepts to multivariate contexts.

Contribution

It proposes novel information-theoretic measures based on copulas for multivariate fractional inaccuracy, including bounds and stochastic ordering properties.

Findings

Established bounds using Frechet-Hoeffding limits

Analyzed behavior under stochastic orderings

Extended measures to co-copula and dual copula forms

Abstract

We introduce novel information-theoretic measures termed the multivariate cumulative copula fractional inaccuracy measure and the multivariate survival copula fractional inaccuracy measure, constructed respectively from multivariate copulas and multivariate survival copulas. These measures generalize the concept of fractional inaccuracy to multivariate settings by incorporating dependence structures through copulas. We establish bounds for these measures using the Frechet-Hoeffding bounds and investigate their behavior under lower and upper orthant stochastic orderings to facilitate comparative analysis. Furthermore, we define the multivariate co-copula fractional inaccuracy measure and the multivariate dual copula fractional inaccuracy measure, derived from the multivariate co-copula and dual copula, respectively, and examine several analogous properties for these extended forms.