In this study, at-site frequency analysis (AFA) of an annual daily maximum rainfall (ADMR) series was carried out using the method of linear moments (L-moments) and their variants such as trimmed linear moments (TL-moments) and higher order linear moments (LH-moments). The ADMR series we investigated was observed at 28 meteorological observatories across Pakistan as retrieved from the Pakistan Meteorological Department (PMD). The basic aim of the study was to fi nd best-fi t (i.e., the most suitable) probability distribution among the class of various probability distributions. Initially different goodness-offi t (GOF) measures such as the Kolmogorov-Smirnov test (KST), Anderson-Darling test (ADT), root mean square error (RMSE) and L-moments ratio diagram (LRD) were applied to determine not only the best-fi t distributions but also the best linear estimation method for AFA. We observed that no single probability distribution could be declared as the best-fi t distribution for all the stations. Five distributions were found to be the most appropriate: generalized extreme value (GEV), three parameter lognormal (LN3), Pearson type III (P3), generalized logistic (GLO), and generalized pareto (GPA). The TL-moments method was also applied for parameter estimation to mitigate the effect of outliers on fi nal estimates. LH-moments were used for estimating the upper part of probability distributions and larger events in the data samples. LH moments alleviate the unwanted affects due to small sample values that may be obvious during estimation of events related to larger return periods. Using different GOF tests, we observed that the L-moments method was best for eight stations, TL-moments with trimming (1, 0), and LH-moments with level η =2, 3, 4 were best for six and 14 stations, respectively. A theoretical relationship between TL-moments and LH-moments was also revisited, which revealed that LH-moments are special cases of TL-moments when we are motivated to make trimming only from the lower side.

For this paper we conducted a regional analysis (RA) of annual peak flows using linear combination of order statistics, i.e., linear-moments (LM) and trimmed linear moments (TLM). Design flood estimates are calculated and compared at different return periods, which are useful for water resources management, including hydrological structures and basin management. The main objective of our study was to compare regional design flood estimates for untrimmed and trimmed samples. LM is the special case of TLM, when we have no trimming from either side. First, regional flood frequency analysis is performed for LM and then for TLM. After initial screening of the annual peak flow series, a discordancy measure was used to diagnose the discordant sites. No site was found to be discordant. For homogeneity of the region, the homogeneity measure "H" was employed using simulation study based on Kappa distribution, and found that the nine sites on the Indus Basin included in the study constitute a single homogeneous region. In this study we used TLM with trimming values (γ, 0), where γ = 1, 2, 3, 4. In order to determine the most appropriate probability distribution for regional quantile estimates, different probability distributions are used, namely: generalized extreme value (GEV), generalized pareto (GPA), generalized logistic (GLO), Pearson type three (PE3), and generalized normal (GNO). L-moments ratio diagram and Z-test as goodness of fit are engaged to identify the most suitable probability distribution. A comparison revealed that GNO is the best distribution for first three cases as (0, 0), (1, 0), and (2, 0), while for the last two cases of (3, 0) and (4, 0) the most appropriate choice is GEV. A simulation study was also carried out to evaluate the performance and robustness of the best fit probability distribution using relative bias (RB) and relative root mean square error (RRMSE).