An Accurate Method for Estimating the Parameters of the Generalized Extreme Value Distribution Using its Moments

El Genidy, Mohammed Mohammed; Hebeshy, Esraa Ahmed; El Desouky, Beih El Sayed; Gomaa, Rabab Sabry

doi:10.21608/ajbas.2023.236538.1183

An Accurate Method for Estimating the Parameters of the Generalized Extreme Value Distribution Using its Moments

Document Type : Review Article

Authors

¹ Department of Mathematics & Computer Science, Faculty of Science, Port Said University, Port Said, Egypt

² Department of Mathematics &amp;amp; Computer Science, Faculty of Science, Port Said University, Port Said, Egypt

³ Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt

10.21608/ajbas.2023.236538.1183

Abstract

Wind speed is a clean energy source that generates electricity. Researchers in this field always need an accurate statistical model to give them high-precision statistical measurements to build power-generation electric systems. This study presents a mathematical model for the maximum wind speed (MWS) in Port Said city by determining the fitting probability distribution. The moment-generating function is used to estimate the Generalized Extreme Value Distribution (GEVD) parameters. The purpose is to obtain a single equation in a single parameter using average, variance, and median formulas of (GEVD), which can be solved numerically. The properties of the cumulative distribution function, method of maximum likelihood estimation (MLE), percentiles, quartiles, nonlinear regression, Anderson-Darling test, Kolmogorov-Smirnov (K-S) test, and Kruskal Wallis test are applied to assess the utility of the proposed distribution. The GEVD is compared with the three-parameter Weibull (W-3P) distribution and with other competing distributions. Finally, the GEVD is the best for modeling MWS data. The statistical measurements of MWS are derived with high accuracy. That will enable researchers to find the best estimation method of the distribution for the actual data.

Keywords