Quantile Tsallis entropy and its dynamic forms for record statistics
摘要
This article introduces a quantile-based Tsallis entropy measure for record data, addressing limitations in various traditional and existing entropy metrics. The proposed measure is rigorously developed through a robust mathematical framework with its applicability to generalized models and demonstrates the distribution-free nature of quantile Tsallis divergence. This study lays the foundation for further exploration of dynamic variants to handle time-varying and state-dependent record data, offering unique insights into characterizing lifetime distributions, and giving alternative expressions, and bounds. Unlike traditional Tsallis residual entropy, the quantile Tsallis residual entropy uniquely identifies the underlying distribution, supported by characterization theorems, broadening the scope of entropy-based analysis in applied domains.