On Relative Cumulative Residual Information Measure and Its Applications

TL;DR

This paper introduces a new measure for quantifying divergence between survival functions, along with estimators and applications in astronomy and medical imaging, supported by simulations and real data analysis.

Contribution

It develops the relative cumulative residual information measure and its dynamic version, with non-parametric estimators and characterization results under proportional hazards.

Findings

Estimators perform well in Monte Carlo simulations.

Application to Gaia DR3 data demonstrates practical utility.

RCRI-based image analysis shows effectiveness in medical imaging.

Abstract

In this paper, we develop a relative cumulative residual information measure (RCRI) that aims to quantify the divergence between two survival functions. The dynamic relative cumulative residual information (DRCRI) measure is also introduced. We establish some characterization results under the proportional hazards model assumption. Additionally, we obtained the non-parametric estimators of RCRI and DRCRI measures based on the kernel density type estimator for the survival function. The effectiveness of the estimators are assessed through an extensive Monte Carlo simulation study. We consider data from the third Gaia data release (Gaia DR3) to demonstrate the use of the proposed measure. For this study, we have collected epoch photometry data for the objects Gaia DR3 4111834567779557376 and Gaia DR3 5090605830056251776. The RCRI-based image analysis is conducted using Chest X-ray data from the publicly available dataset.