Hybrid estimation using L-moments for r -largest order statistics approach

Estimating high quantiles, such as the T-year return level, is important in risk analysis and infrastructure design. The generalized extreme value distribution based on block maxima has been widely used for this purpose, but has been criticized for its inefficient use of data. The r-largest order statistics (rLOS) approach incorporates more observations from each block and can improve estimation precision. Maximum likelihood estimation (MLE) is commonly used for rLOS models, but tends to overestimate high quantiles, particularly for small samples with heavy tails. To mitigate this issue, we develop a method based on the L-moment estimator (LME) for rLOS while retaining the advantages of the LME. Specifically, we propose a weighted LME (WeLMET) and a hybrid estimator combining WeLMET with MLE. Simulation results show that the hybrid estimator is nearly unbiased and has lower mean squared error than competing methods for return-level estimation with small samples and heavy right tails. The proposed methods are illustrated using annual r-largest daily rainfall data from Maha Sarakham, Thailand.