A Simulation Study on Bias Effects in Probability Distribution Fitting for Rainfall Extremes

Abstract

Accurate modeling of extreme rainfall is essential for hydrological planning and disaster mitigation in Malaysia. However, biases in rainfall data, whether due to measurement errors or model outputs, can distort the fit of probability distributions used in extreme value analysis. This study simulates synthetic extreme rainfall data under four systematic bias scenarios: additive, multiplicative, combined, and non-linear. Each dataset was generated via Monte Carlo simulation to mimic the annual characteristics of extreme rainfall. Four probability distributions, which are Gamma, Weibull, Burr Type XII, and Kappa, were fitted to the biased and bias-corrected datasets, with parameters estimated using the Maximum Likelihood Estimation (MLE) method. Quantile Mapping (QM) was employed to correct the biases prior to fitting. Model performance was assessed using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Nash-Sutcliffe Efficiency (NSE), Kling-Gupta Efficiency (KGE), and Goodness-of-Fit (GoF) tests. Accordingly, the findings reveal that the Kappa distribution consistently performs best under additive and combined biases. By contrast, the Burr Type XII distribution outperforms others under non-linear scenarios. While Weibull yields low fitting errors for multiplicative biases, it fails to pass statistical fit tests. The gamma distribution performs poorly across all scenarios. Overall, these results highlight the importance of selecting appropriate distribution models following bias correction, with Kappa and Burr identified as robust choices for modeling extreme rainfall under biased conditions in Malaysia.