(untitled) (International Journal of Statistical Sciences, 2025)
Proper rainfall modeling is important for efficient water resource management, strategic agricultural planning and formulating disaster preparedness plans, particularly in climate-sensitive areas like northwest Bangladesh. This study develops a hybrid approach that integrates probabilistic distribution fitting with machine learning techniques to improve accuracy and forecast rainfall. For this purpose, monthly time series data collected by Bangladesh meteorological department (BMD) of three meteorological stations of northwest Bangladesh, namely, Rajshahi, Ishurdi and Bogura for the period 1964-2023 were analyzed. The time series rainfall data was evaluated models of probability distributions as Log-Normal, Log-Pearson III, Pearson III, GEV, Gamma, Weibull, and Exponential using AIC and BIC criteria, alongside Random Forest and hybrid models for forecasting. The spatial analysis identified Log-Normal (LN2) as the most suitable distribution for Rajshahi (AIC = 739.44), Log-Pearson III for Ishurdi (AIC = 768.15), and Pearson III for Bogura (AIC = 761.04). Forecasts indicate an upward trend in extreme rainfall events, with Ishurdi demonstrating the highest inter annual variability, including projected peaks exceeding 600 mm. Among the forecasting approaches, the hybrid model integrating Random Forest and probabilistic distribution fitting achieved superior performance, particularly in Ishurdi (RMSE = 127.78, MAPE = 34.71%). In contrast, the LN2 and Pearson III distributions yielded the most accurate predictions for Rajshahi and Bogura, respectively. These results highlight how regional model selection can improve rainfall forecasting accuracy and how crucial these methods are for guiding water resource management in highly variable and data-constrained environments, supporting precision agriculture, developing early warning systems, and forming climate-resilient policy. International Journal of Statistical Sciences, Vol. 25(2), November, 2025, pp 127-141