Statistical Modeling of Rainfall in Iraq: A Comparative Study of Classical and Flexible Probability Distributions

Abstract

Probabilistic modeling of rainfall data is an effective framework for analyzing the stochastic behavior of hydrological processes. This research involved fitting several distributions to the observed rainfall data in Iraq including the Gamma, Lognormal, Weibull, Generalized Weibull, GEV, and Nakagami distributions. The maximum likelihood method was used for parameter estimation. The adequacy of the model was evaluated through a series of goodness-of-fit statistics which include coefficient of determination, root mean square error, information criteria as well as the Kolmogorov–Smirnov test. The analysis shows the Gamma distribution performed best overall, with Weibull and GEV following closely behind, while Lognormal and Generalized Weibull were clearly poor fits to the observed rainfall data. Understanding streamflow distributions is vital for predicting streamflow behavior and improving hydrological forecasts. Furthermore, proper quantification can be useful for ecological management and mitigation efforts. When considering statistics, the research proves the impact of the Gamma distribution in modeling positively skewed rainfall. Thus, this can be used to conduct further stochastic analysis in applied hydrology.