An alternate double-bounded distribution for environmental variables and its possible application to wind speed modeling

Abstract

Natural phenomena such as wind speed, flood levels, precipitation, and many others exhibit bounded behavior on both ends due to physical constraints. This paper introduces an alternative Generalized Double Bounded Distribution (GDBD), developed using a principle similar to the extreme value theory to model such events. The proposed distribution is validated against the widely used Kumaraswamy distribution through various datasets, demonstrating its suitability as a robust alternative double-bounded distribution. The application of the proposed distribution is presented by modeling the annual maximum wind speed. Recordings from 12 stations across the Indian subcontinent are utilized for this purpose and assessed against the Generalized Extreme Value (GEV) distribution. The performance is assessed in two key aspects: i) interpolation behavior using the Kolmogorov–Smirnov (K-S) test to evaluate the quality of fit, and ii) extrapolation behavior, by comparing the long-tail predictions against the simulated wind speed data generated via the Markov Chain model. In addition to the point estimate of long-tail quantiles, the proposed distribution exhibits significantly reduced uncertainty when compared with the GEV distribution, as indicated by narrower confidence intervals at long return periods. The associated quantiles at higher return periods are noted to be underestimated by GEV distribution when compared with the proposed distribution for a few stations, which may also be a concern from the structural assessment point of view. Overall, the proposed GDBD is likely to be a viable alternative for hazard assessment and structural design.