Generalized Weighted Survival and Failure Entropies and their Dynamic Versions

TL;DR

This paper introduces weighted generalized survival and failure entropies, explores their properties and dynamic versions, characterizes specific distributions, and proposes a new test for exponentiality based on empirical entropy differences.

Contribution

It proposes new weighted entropy measures, their dynamic forms, and a novel test for exponentiality, extending existing entropy-based methods.

Findings

Characterization of Rayleigh and power distributions using dynamic entropies.

Development of empirical entropy measures and a test for exponentiality.

Derivation of properties and bounds for the proposed entropy measures.

Abstract

The weighted forms of generalized survival and failure entropies of order ($\alpha,\beta$) are proposed and some properties are obtained. We further propose the dynamic versions of weighted generalized survival and failures entropies and obtained some properties and bounds. Characterization for Rayleigh and power distributions are done by dynamic weighted generalized entropies. We further consider the empirical versions of generalized weighted survival and failure entropies and using the difference between theoretical and empirical survival entropies a test for exponentiality is considered.