On the Study of Weighted Fractional Cumulative Residual Inaccuracy and its Dynamical Version with Applications

TL;DR

This paper introduces the Weighted Fractional Cumulative Residual Inaccuracy (WFCRI), a new measure for quantifying uncertainty and inaccuracy in systems, with theoretical properties, dynamic behavior, estimation methods, and practical applications.

Contribution

It presents the novel WFCRI measure, explores its properties, dynamic version, estimation method, and demonstrates its application to chaotic systems and real data.

Findings

WFCRI has well-defined fundamental properties and bounds.

The dynamic WFCRI effectively characterizes chaotic dynamics.

The empirical estimation method performs well in simulations.

Abstract

In recent years, there has been a growing interest in information measures that quantify inaccuracy and uncertainty in systems. In this paper, we introduce a novel concept called the Weighted Fractional Cumulative Residual Inaccuracy (WFCRI). We develop several fundamental properties of WFCRI and establish important bounds that reveal its analytical behavior. Further, we examine the behavior of WFCRI under a mixture hazard model. A dynamic version of WFCRI also proposed and studied its behavior under proportional hazard rate model. An empirical estimation method for WFCRI under the proportional hazard rate model framework is also proposed, and its performance is evaluated through simulation studies. Finally, we demonstrate the utility of WFCRI measure in characterizing chaotic dynamics by applying it to the Ricker and cubic maps. The proposed measure is also applied to real data to assess the uncertainty.