Two-Parameter Probability Distributions: Methods, Techniques and Comparative Analysis

Abstract

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).

Keywords

• parameter estimation
• probability distribution
• relative errors
• gamma
• log-normal
• Gumbel