Relative Cumulative Residual Information Measure

In this paper, we develop a relative cumulative residual information (RCRI) measure that intends 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 the data from the third Gaia data release (Gaia DR3) for demonstrating 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.