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Being the parent distribution in Romania, the Pearson III distribution (PE3) is one of the statistical distributions that is most frequently used in flood frequency analysis (FFA). All the components required for the simple implementation of PE3 distribution in FFA are presented in this manuscript. The estimated methods and exact and approximate relationships for estimating the parameters and frequency factors particular to the distribution are described. All of these factors are used to identify maximum flows with various annual exceedance probabilities, using data collected at the 6 rivers with different morphometric characteristics and different lengths of data series. Five parameter estimation techniques are used in this comparative analysis, i.e. the method of ordinary moments (MOM), the method of linear moments (L-moments), the high-order linear moments method (LH-moments), the method of maximum likelihood (MLE) and the method of least squares (LSM). Given the results, it can be assumed that the L-moments approach is more reliable, stable, robust and less sensitive to variations in recorded data lengths, as well as to the presence of outliers. [ABSTRACT FROM AUTHOR]

This study examines all of the equations necessary to derive the parameters for seven probability distributions of three parameters typically used in flood frequency research, namely the Pearson III (PE3), the generalized extreme value (GEV), the Weibull (W3), the log-normal (LN3), the generalized Pareto Type II (PG), the Rayleigh (RY) and the log-logistic (LL3) distributions, using the higher-order linear moments method (LH-moments). The analysis represents the expansion of previous research whose results were presented in previous materials, and is part of hydrological research aimed at developing a standard for calculating maximum flows based on L-moments and LH-moments. The given methods for calculating the parameters of the examined distributions are used to calculate the maximum flows on Romania's Prigor River. For both methods, the criterion for selecting the most suitable distribution is represented by the diagram of the L-skewness–L-kurtosis and LH-skewness–LH-kurtosis. The results for Prigor River show that the PG distribution is the best model for the L-moments method, the theoretical values of the statistical indicators being 0.399 and 0.221. The RY distribution is the best model for the LH-moments technique, with values of 0.398 and 0.192 for the two statistical indicators. [ABSTRACT FROM AUTHOR]

Considering the wide applicability of two-parameter distributions in the frequency analysis of extreme events, this article presents new elements regarding the use of thirteen two-parameter probability distributions, using three parameter estimation methods. All the necessary elements for the application of these distributions are presented using the method of ordinary moments (MOM), the method of linear moments (L-moments) and the method of high order linear moments (LH-moments). Only these three methods are analyzed, because they are usually applied in the analysis regarding the regionalization of extreme events. As a case study, the frequency analysis of the maximum annual flows on the Siret River, Lungoci station, Romania, was made. For the recommended methods (L- and LH-moments), from the thirteen analyzed distributions, the log-normal distribution had the best results, with the theoretical values L-coefficient of variation and L-kurtosis (0.297, 0.192, 0.323, 0.185, 0.336, and 0.185) best approximating the corresponding values of the recorded data (0.339, 0.185, 0.233, 0.199, 0.198, and 0.205). [ABSTRACT FROM AUTHOR]