Three-parameter lognormal distribution: parametric estimation using l-moment and tl-moment approach

Abstract

The three-parameter lognormal (LN3) distribution has been applied to the frequency analysis of flood events. L-moment and TL-moment methods are applied in estimating parameters of the LN3 distribution which are L-moment, η = 0 and TL-moment, η = 1, 2, 3, and 4 to the LN3 distribution. A simulation study is conducted in this paper by fitting this distribution to generate LN3 and non LN3 samples. Relative Root Mean Square Error (RRMSE) and relative bias are evaluated to illustrate the performance of this distribution. The performance of TL-moments approach was compared with L-moments based on the streamflow data from Sg. Trolak and Sg. Slim which are located in Perak, Malaysia. The results showed that TL-moments approach produced a better result at high quantile estimation compared to L-moments.