Integrating a Novel Kumaraswamy-Teissier Distribution with VARMA: A Hybrid Framework for Rainfall Modeling and Forecasting in the Northwest Himalayas

Abstract

Rainfall modeling in mountainous regions requires flexible statistical tools capable of capturing strong skewness and extremes. This study proposes a novel hybrid KTD-VARMA framework to address this challenge. The framework first introduces the Kumaraswamy-Teissier Distribution (KTD), a new three-parameter model derived via the Kumaraswamy-G generator, to statistically characterize extreme rainfall. Its properties are derived, and parameters are estimated via maximum likelihood, maximum product spacing, and a Bayesian (MCMC) approach along with credible and HPD intervals. The KTD provides a superior fit compared to its sub-models. The return-period analysis highlights clear spatial contrasts: Dehradun experiences the most frequent extremes, Mandi and Kangra exhibit moderate extremal behavior, while Shimla and Nainital display long return periods for extreme monthly totals. Further, the KTD serves as a normalizing transformation for the skewed rainfall series and KTD-transformed data are then modeled using a Vector Autoregressive Moving Average (VARMA) model to capture spatio-temporal dependencies. This integrated methodology, presented here for the first time, yields more accurate forecasts after seasonal adjustment than models using raw data or univariate ARIMA, with VARMA achieving the lowest RMSE. The work establishes the KTD-VARMA framework as a comprehensive tool for both extreme value analysis and improved multi-site forecasting, providing a robust approach for hydrological risk assessment in mountainous regions.