Fractional Cumulative Residual Entropy in the Quantile Framework and its Applications in the Financial Data

TL;DR

This paper introduces a quantile-based fractional cumulative residual entropy (FCRE) and explores its properties and applications, especially in situations where the distribution function is not explicitly available but the quantile function is.

Contribution

The paper develops a novel quantile-based FCRE framework, extending the traditional distribution function approach and demonstrating its usefulness in applied fields.

Findings

Defined a new quantile-based FCRE and its dynamic version.

Derived properties and theoretical results for the quantile-based FCRE.

Showcased applications in financial data analysis.

Abstract

Fractional cumulative residual entropy (FCRE) is a powerful tool for the analysis of complex systems. Most of the theoretical results and applications related to the FCRE 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 this, in the present study we introduce a quantile-based FCRE, its dynamic version and their various properties and examine their usefulness in different applied fields.