Statistical Modeling of Indus River Outflow at Tarbela Dam using Generalized Gumbel Type 2 Distribution

Abstract

Abstract The Indus River, a lifeline for Pakistan, holds paramount significance for its geography, history, and economy. This research delves into a comprehensive analysis of the river's behavior by introducing a novel statistical framework. Leveraging the Gumbel Type 2 distribution and the Rayleigh distribution, a new generalized Gumbel Type 2 (GG2) distribution is derived, and used for modeling the data about the river's outflow at the Tarbela Dam during 2020–2021. Our study contributes to the understanding of the complex dynamics of the Indus River, aiding in the sustainable management of its resources. The GG2 distribution, designed for extreme value events, adept at modeling positive-valued variables, were combined to model the intricate characteristics of the river's flow. Parameters were estimated using both classical and Bayesian methods, enhancing the accuracy and reliability of our findings. The incorporation of Bayesian techniques adds robustness to our parameter estimates and allows for a more comprehensive uncertainty analysis. The results not only deepen our understanding of the river's behavior but also offer insights crucial for infrastructure planning, flood control, and resource allocation.