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

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. Combining 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. The GG2 distribution, designed for extreme value events, adept at modeling positive-valued variables, were combined to model the complexed characteristics of the river's flow. Parameters are estimated using both classical and Bayesian methods, enhancing the accuracy and reliability of our findings. The Bayse estimators are not in the closed form expression, hence the Tierney-Kadane approximation technique is used. Through simulation study and analysis, the data set of overflows of the river Indus over Tarbela Dam, the Bayes estimators demonstrate superior performance in minimizing risk compared to classical estimators. It is shown graphically that that our proposed distribution performs better than its competitor distributions. 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.