Simulation-based modeling of rainfall data: addressing zeros and extremes
摘要
Rainfall data present a unique statistical challenge due to their characteristic structure, dominated by a large proportion of zero values and a heavy-tailed distribution of extremes. These features complicate conventional modeling approaches, particularly when seeking to generate realistic synthetic datasets for simulation-based studies. This paper addresses the dual challenge of zero inflation and tail extremity by proposing a simulation framework grounded in threshold-based extreme value theory and tailored to replicate real-world rainfall behavior. We investigate and compare four modeling strategies: the Extended Generalized Pareto Distribution (EGPD), composite, truncated, and a probabilistically structured mixed model. The study is anchored in a robust threshold selection method that incorporates L-moments and the Anderson–Darling goodness-of-fit test, ensuring stability across datasets with varying proportions of zeros. Using the South West England daily rainfall dataset as a reference, synthetic datasets are generated under different sample sizes, and model performance is evaluated through bias, standard error, and root mean square error of the estimated threshold and tail parameters. Results show that all models capture rainfall characteristics to varying degrees, but the mixed model consistently balances bias control, estimation stability, and fit accuracy across scenarios. Threshold and return level uncertainties, assessed via the bootstrap percentile method, further validate the practical reliability of the models. This work offers a computationally accessible yet statistically rigorous approach to modeling rainfall data, supporting more informed simulation studies in hydrology, infrastructure planning, and climate risk assessment.