On Weighted Generalized Entropy for Double Truncated Distribution

TL;DR

This paper introduces a new weighted generalized interval entropy measure for double truncated distributions, exploring its properties and applications in reliability analysis with simulations and real data.

Contribution

It proposes the weighted generalized interval entropy (WGIE) for double truncated distributions and studies its properties and applications in reliability modeling.

Findings

WGIE has monotonicity, bounds, and uniqueness properties.

Simulation results demonstrate effective estimation of WGIE.

Application to real data shows WGIE's usefulness in reliability analysis.

Abstract

The notion of weighted Renyi's entropy for truncated random variables has recently been proposed in the information-theoretic literature. In this paper, we introduce a generalized measure of it for double truncated distribution, namely weighted generalized interval entropy (WGIE), and study it in the context of reliability analysis. Several properties, including monotonicity, bounds and uniqueness of WGIE are investigated. Moreover, a simulation study is carried out to demonstrate the performance of the estimates of the proposed measure using simulated and real data sets. The role of WGIE in reliability modeling has also been investigated for a real-life problem.