Fractional cumulative Residual Inaccuracy in the Quantile Framework and its Appications

TL;DR

This paper introduces a quantile-based fractional cumulative residual inaccuracy (FCRI) measure, extending its applicability to cases where the distribution function is unavailable but the quantile function is known, with practical applications in chaotic systems and financial data.

Contribution

It develops a novel quantile-based FCRI measure, analyzes its properties, and demonstrates its effectiveness through simulations and real-world data comparisons.

Findings

Quantile-based FCRI effectively measures discrepancies between systems.

Simulation studies validate the estimation method.

Application to Nifty 50 data shows practical utility.

Abstract

Fractional cumulative residual inaccuracy (FCRI) measure allows to determine regions of discrepancy between systems, depending on their respective fractional and chaotic map parameters. Most of the theoretical results and applications related to the FCRI of the lifetime random variable are based on the distribution function approach. However, there are situations in which the distribution function may not be available in explicit form but has a closed-form quantile function (QF), an alternative method of representing a probability distribution. Motivated by these, the present study is devoted to introduce a quantile-based FCRI and study its various properties. We also deal with non-parametric estimation of quantile-based FCRI and examine its validity using simulation studies and illustrate its usefulness in measuring the discrepancy between chaotic systems and in measuring the discrepancy in two different time regimes using Nifty 50 dataset.