Robust analysis of spatio-temporal inequality with Inverse entropy

Abstract

This study introduces Inverse entropy, a novel metric for spatio-temporal inequality that extends traditional measures such as Shannon entropy and the Gini coefficient. Unlike dispersion-based indices, it focuses on temporal concentration and employs a decomposition framework to disentangle structural, transversal, and allocative components, offering deeper insights into inequality dynamics. Monte Carlo simulations validate its robustness across skewed and noisy distributions, demonstrating superior sensitivity, monotonicity, and scalability compared to traditional inequality and concentration measures. An empirical analysis of 106 Spanish tourism destinations (2005–2019) reveals significant temporal disparities, with transversal components emerging as key drivers of seasonal demand variability. The results provide actionable insights for policymakers, addressing structural dependencies and allocative inefficiencies to optimise resource allocation. The computational implementation ensures reproducibility using R, enabling large-scale analyses. Beyond tourism, Inverse entropy is applicable to energy demand, transportation, and retail forecasting.