Parameter estimate for three-parameter kappa distribution using LHmoments approach

Abstract

The method of higher-order L-moments (LH-moment) was proposed as a more robust alternative compared to classical L-moments to characterize extreme events. The new derivation will be done for Mielke-Johnson’s Kappa and Three-Parameters Kappa Type-II (K3D-II) distributions based on the LH-moments approach. The data of maximum monthly rainfall for Embong station in Terengganu were used as a case study. The analyses were conducted using the classical L-moments method with η=0 and LH-moments methods with η=1, η=2, η=3 and η=4 for a complete data series and upper parts of the distributions. The most suitable distributions were determined based on the Mean Absolute Deviation Index (MADI), Mean Square Deviation Index (MSDI), and Correlation (r). Also, L-moment and LH-moment ratio diagrams were used to represent visual proofs of the results. The analysis showed that LH-moments methods at a higher order of K3D-II distribution best fit the data of maximum monthly rainfalls for the Embong station for the upper parts of the distribution compared to L-moments. The results also proved that whenever η increases, LH-moments reflect more and more characteristics of the upper part of the distribution. This seems to suggest that LH-moments estimates for the upper part of the distribution events are superior to L-moments in fitting the data of maximum monthly rainfalls.