Non-stationary flood frequency analysis (NFFA) plays an important role in addressing the issue of the stationary assumption (independent and identically distributed flood series) that is no longer valid in infrastructure-designed methods. This confirms the necessity of developing new statistical models in order to identify the change of probability functions over time and obtain a consistent flood estimation method in NFFA. The method of Trimmed L-moments (TL-moments) with time covariate is confronted with the L-moment method for the stationary and non-stationary generalized extreme value (GEV) models. The aims of the study are to investigate the behavior of the proposed TL-moments method in the presence of NFFA and applying the method along with GEV distribution. Comparisons of the methods are made by Monte Carlo simulations and bootstrap-based method. The simulation study showed the better performance of most levels of TL-moments method, which is TL(η,0), (η = 2, 3, 4) than the L-moment method for all models (GEV1, GEV2, and GEV3). The TL-moment method provides more efficient quantile estimates than other methods in flood quantiles estimated at higher return periods. Thus, the TL-moments method can produce better estimation results since the L-moment eliminates lowest value and gives more weight to the largest value which provides important information.
Understand the extreme volatility in the market is important for the investor to make a correct prediction. This paper evaluated the performance of generalized lambda distribution (GLD) by comparing with the popular probability distribution namely generalized extreme value (GEV), Generalized logistic (GLO), generalized Pareto (GPA), and Pearson (PE3) using Kuala Lumpur composite index stock return data. The parameter for each distribution estimated using the L-moment method. Based on k-sample Anderson darling goodness of fit test, GLD performs well in weekly maximum and minimum period. Evidence for preferring GLD as an alternative to extreme value theory distribution also described.
Abstract. Extreme flood event are among environmental events with the most disastrous consequences for human society. This paper deals with the identification of homogeneous regions through important steps in the regional frequency analysis. Streamflow totals measured at 70 stations over 1960-2009. The cluster analysis uses kriging technique and shows three regions of streamflow in Peninsular Malaysia. The homogeneity test of L-moments shows that some of these regions are homogeneous. Using the goodness-of-fit test, Z-Dist, the regional frequency distribution functions for each group are then selected. In this study, five three parameter distributions generalized logistic (GLO), generalized extreme-value (GEV), generalized pareto distributions (GPA), Pearson Type III (P3), and three parameter Lognormal (LN3) were fitted to the three homogeneous regions.
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.
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