Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Evaluation of Various Generalized Pareto Probability Distributions for Flood Frequency Analysis

Version 1 : Received: 28 March 2023 / Approved: 29 March 2023 / Online: 29 March 2023 (02:29:25 CEST)

A peer-reviewed article of this Preprint also exists.

Anghel, C.G.; Ilinca, C. Evaluation of Various Generalized Pareto Probability Distributions for Flood Frequency Analysis. Water 2023, 15, 1557. Anghel, C.G.; Ilinca, C. Evaluation of Various Generalized Pareto Probability Distributions for Flood Frequency Analysis. Water 2023, 15, 1557.

## Abstract

This article analyzes 6 probability distributions from the Generalized Pareto family, with 3, 4 and 5 parameters, with main purpose to identify other distributions from this family with applicability in flood frequency analysis compared to the distribution already used in the literature from this family such as Generalized Pareto Type II and Wakeby. This analysis is part of a larger and more complex research carried out in the Faculty of Hydrotechnics regarding the elaboration of a norm for flood frequency analysis using the linear moments method. In Romania, the standard method of parameter estimation is the method of ordinary moments, thus the transition from this method to the method of linear moments is desired. All the necessary elements for the distributions use are presented like, the probability density functions, the complementary cumulative distribution functions, the quantile functions, the exact and approximate relations for estimating parameters, for both methods of parameters estimation. All these elements are necessary for a proper transition between the two methods, especially since the use of the method of ordinary moments is done by choosing the skewness of the observed data depending on the origin of the maximum flows. A flood frequency analysis case study, using annual maximum and annual exceedance series, was carried out for the Prigor river, to numerically present the analyzed distributions. The performance of this distributions is evaluated using relative mean error, relative absolute error and linear moments diagram.

## Keywords

floods; frequency analysis; extreme value statistics; Pareto; Wakeby; estimation parameters; approximate form; method of ordinary moments; method of linear moments

## Subject

Environmental and Earth Sciences, Water Science and Technology