Uniformity Testing and Estimation of Generalized Exponential Uncertainty in Human Health Analytics

The entropy function, as a measure of information and uncertainty, has been widely applied in various scientific disciplines. One notable extension of entropy is exponential entropy, which finds applications in fields such as optimization, image segmentation, and fuzzy set theory. In this paper, we explore the continuous case of generalized exponential entropy and analyze its behavior under symmetric and asymmetric probability distributions. Particular emphasis is placed on illustrating the role of symmetry through analytical results and graphical representations, including comparisons of entropy curves for symmetric and skewed distributions. Moreover, we investigate the relationship between the proposed entropy model and other information-theoretic measures such as entropy and extropy. Several non-parametric estimation techniques are studied, and their performance is evaluated using Monte Carlo simulations, highlighting asymptotic properties and the emergence of normality, an aspect closely related to distributional symmetry. Furthermore, the consistency and biases of the estimation methods, which rely on kernel estimation with (Formula presented.) -mixing dependent data, are presented. Additionally, numerical calculations based on simulation and medical real data are applied. Finally, a test of uniformity using different test statistics is given.