Probabilistic modeling of bounded proportional data of physical–recreational activities in urban parks

Probability distribution modeling for bounded data provides a probabilistic representation of real-world processes. However, data bounded within the unit interval pose statistical challenges due to asymmetry and boundary point masses. This study investigates the suitability of probability distributions for modeling the proportion of visitors engaged in physical–recreational activities (PRAs) in parks of Pune and develops a framework for fitting and assessing these distributions. Classical Gaussian and non-Gaussian distributions were fitted to the proportion of PRA from 88 urban parks of Pune. These models were evaluated using information criteria (Akaike Information Criterion [AIC]/Corrected Akaike Information Criterion [AICC]/Bayesian Information Criterion [BIC]), Graphical diagnostics, and a parametric bootstrap Kolmogorov–Smirnov (K–S) goodness-of-fit test. The Zero–One Inflated Beta (ZOIB) distribution provided the most suitable representation of the PRA proportions among all the selected distributions, enabling a parametric characterization through its shape parameters and moments. ZOIB regression and likelihood ratio (LR) test results (LR = 12.1444, p = 0.734) indicated no statistically significant impact of zones on PRA proportions, demonstrating consistent park usage pattern across zones. The fitted ZOIB results showed that overall, 67% of visitors were engaged in PRA. It highlighted park visitors’ behavior toward PRA and hence the importance of incorporating demand for physical–recreational activities into urban park infrastructure planning and management. This evidence supports planning for inclusive and accessible urban green spaces (public parks), contributing to Sustainable Development Goal (SDG) 11, particularly Target 11.7 (inclusive and equitable access to green spaces).