On residual cumulative generalized exponential entropy and its application in human health

Numerous adaptations of traditional entropy concepts and their residual counterparts have emerged in statistical research. While some methodologies incorporate supplementary variables or reshape foundational assumptions, many ultimately align with conventional formulations. This study introduces a novel extension termed residual cumulative generalized exponential entropy to broaden the scope of residual cumulative entropy for continuous distributions. Key attributes of the proposed measure include non-negativity, bounds, its relationship to the continuous entropy measure, and stochastic comparisons. Practical implementations are demonstrated through case studies involving established probability models. Additionally, insights into order statistics are derived to characterize the measure's theoretical underpinnings. The residual cumulative generalized exponential entropy framework bridges concepts such as Bayesian risk assessment and excess wealth ordering. For empirical implementation, non-parametric estimation strategies are devised using data-driven approximations of residual cumulative generalized exponential entropy, with two distinct estimators of the cumulative distribution function evaluated. A practical application is showcased, using clinical diabetes data. The study further explores the role of generalized exponential entropy in identifying distributional symmetry, mainly through its application to uniform distributions to pinpoint symmetry thresholds in ordered data. Finally, the utility of generalized exponential entropy is examined in pattern analysis, with a diabetes dataset serving as a benchmark for evaluating its classification performance.