The Relative Information Generating Function-A Quantile Approach

TL;DR

This paper introduces a quantile-based relative information generating function that unifies entropy and divergence measures, including Kullback-Leibler divergence, with applications to residual and past lifetimes, and provides a non-parametric estimator validated through simulations and real data.

Contribution

It presents a novel quantile-based information generating function, extending existing divergence measures, along with a non-parametric estimator and practical applications.

Findings

The proposed function encompasses Kullback-Leibler divergence.

The non-parametric estimator performs well in simulations.

Application to real data demonstrates practical utility.

Abstract

Information generating functions have been used for generating various entropy and divergence measures. In the present work, we introduce quantile based relative information generating function and study its properties. The proposed generating function provides well-known Kullback-Leibler divergence measure. The quantile based relative information generating function for residual and past lifetimes are presented. A non parametric estimator for the function is derived. A simulation study is conducted to assess performance of the estimators. Finally, the proposed method is applied to a real life data.