An Accurate Method for Estimating the Parameters of the Generalized Extreme Value Distribution Using its Moments
El Genidy, M., Hebeshy, E., El Desouky, B., Gomaa, R. (2024). An Accurate Method for Estimating the Parameters of the Generalized Extreme Value Distribution Using its Moments. EKB Journal Management System, 5(2), 190-207. doi: 10.21608/ajbas.2023.236538.1183
Mohammed Mohammed El Genidy; Esraa Ahmed Hebeshy; Beih El Sayed El Desouky; Rabab Sabry Gomaa. "An Accurate Method for Estimating the Parameters of the Generalized Extreme Value Distribution Using its Moments". EKB Journal Management System, 5, 2, 2024, 190-207. doi: 10.21608/ajbas.2023.236538.1183
El Genidy, M., Hebeshy, E., El Desouky, B., Gomaa, R. (2024). 'An Accurate Method for Estimating the Parameters of the Generalized Extreme Value Distribution Using its Moments', EKB Journal Management System, 5(2), pp. 190-207. doi: 10.21608/ajbas.2023.236538.1183
El Genidy, M., Hebeshy, E., El Desouky, B., Gomaa, R. An Accurate Method for Estimating the Parameters of the Generalized Extreme Value Distribution Using its Moments. EKB Journal Management System, 2024; 5(2): 190-207. doi: 10.21608/ajbas.2023.236538.1183

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

Alfarama Journal of Basic & Applied Sciences
Volume 5, Issue 2, April 2024, Page 190-207  XML PDF (1.15 MB)
Document Type: Review Article
DOI: 10.21608/ajbas.2023.236538.1183
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Authors
Mohammed Mohammed El Genidyorcid 1; Esraa Ahmed Hebeshy email 2; Beih El Sayed El Desouky3; Rabab Sabry Gomaa3
1Department of Mathematics & Computer Science, Faculty of Science, Port Said University, Port Said, Egypt
2Department of Mathematics & Computer Science, Faculty of Science, Port Said University, Port Said, Egypt
3Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
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
Maximum wind speed; generalized extreme value distribution; three-parameter Weibull distribution; moment generating function; maximum likelihood estimation
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