The quantification of randomness, uncertainty, and diversity is a central challenge in information theory and applied sciences. While generalized entropies offer flexibility, they often lack tractable maximum entropy distributions or universal normalization. In this study, we introduce a novel randomness measure, \(\zeta _C(\textbf{p})\) , derived from the Chakravarty inequality index using the framework of pseudometric theory. Unlike classical entropies, this measure is strictly bounded in the unit interval [0, 1], ensuring immediate interpretability across systems of varying dimensions. Its defining feature is the tunable sensitivity parameter \(\alpha \) , which allows for continuous interpolation between support-sensitive behavior (akin to Hartley entropy) and concentration-sensitive behavior (akin to Shannon entropy). We rigorously establish its axiomatic foundations–satisfying continuity, symmetry, and maximality–and derive its associated maximum entropy distribution, yielding a tractable q-exponential form capable of modeling heavy-tailed systems. To ensure practical reliability, we validate the measure’s finite-sample performance through extensive Monte Carlo robustness simulations and bootstrap uncertainty quantification. Empirical applications across diverse domains–including microbial species evenness, SAARC regional economic analysis, and South African income distribution data–confirm that \(\zeta _C(\textbf{p})\) captures subtle structural nuances, such as rare species detection and extreme wealth concentration, that traditional logarithmic measures often overlook. These theoretical and empirical results establish \(\zeta _C(\textbf{p})\) as a robust, highly adaptable tool for complex system modeling.
