Further aspects of information-generating function of order statistics with health application in symmetry of chronic disease management

This investigation aimed to explore novel theoretical aspects and applications of the information-generating function measure for order statistics. We developed fundamental properties and established stochastic ordering relationships based on this information-theoretic measure. Our analysis demonstrated that when two order statistics share identical information-generating measures, their underlying parent distributions can be uniquely identified. We implemented our proposed measure to characterize the exponential distribution. Moreover, we derived bounds and investigated monotonicity properties for these functional measures. The study further examined how information-generating functions characterize distributional symmetry, with particular applications to uniform and normal distributions for identifying symmetry points of order statistics. Building on these theoretical foundations, we proposed a new symmetry test statistic derived from the information-generating properties of the order statistics. Using comprehensive Monte Carlo simulations, we evaluated the test's statistical power against existing alternatives. The present results demonstrated superior performance across various asymmetric distributional alternatives. The practical utility of our methodology is illustrated through an empirical analysis of chronic disease prevalence data.