International Journal of Science, Engineering and TechnologyAuthors: Muhammad Nura, Zahrahtul Amani Zakaria
Abstract: Strong parameter estimation for flexible multi-parameter distributions is essential for hydrological analysis of extreme values in a heavy-tailed, contaminated environment. Even though the Three-parameter Kappa Type-II (K3D-II) distribution is flexible for tail modeling, traditional L-moments and maximum likelihood estimation (MLE) are not very stable and should be used with more robust methods for reliable regional frequency analysis. A trimmed L-moment (TL-moment) estimation framework was developed for K3D-II. Closed-form expressions for the first four TL-moments were derived from the quantile function. Parameters were estimated sequentially: the shape parameter via bounded root-finding using TL-skewness, followed by direct estimation of location and scale. A Monte Carlo simulation was used to evaluate performance [10,000 replications] across light-, moderate-, and heavy-tailed regimes, sample sizes, and contamination levels of 0, 5, 10, and 20% based on Bias, RMSE, and relative efficiency. The TL-moment estimator was more stable and less sensitive to extremes as compared to L-moments or MLE. TL-moments preserved the same bias =0.15, RMSE=0.20, and 90 percent efficiency, and MLE worsened (bias=0.60, RMSE=0.65, and efficiency=50 percent). Best results were obtained with the shape parameter under heavy-tailed conditions. Moderate symmetric trimming TL (1,1) provided the most satisfactory balance of robustness, efficiency, and extreme-quantile reliability. The TL-moment framework improves robustness, identifiability, and numerical stability in K3D-II estimation. It builds on classical L-moment theory by adding resistance to contamination via trimming, supporting reliable at-site and regional hydrological frequency analysis.
