(49-1) 15 * << * >> * Русский * English * Содержание * Все выпуски
Renewed empirical formulas for estimating Weibull distribution parameters
D.G. Asatryan 1,2
1 Institute for Informatics and Automation Problems of NAS RA,
0014, Armenia, Yerevan, P. Sevaki street, 1;
2 Russian-Armenian University,
0052, Armenia, Yerevan, O. Emini street, 123
PDF, 626 kB
DOI: 10.18287/2412-6179-CO-1475
Страницы: 121-124.
Язык статьи: English.
Аннотация:
The empirical formulas proposed in the literature for estimating the parameters of a two-parameter Weibull distribution, obtained using the equations of the moment method, are considered. It is noted that the formulas used to estimate the shape parameter take the form of various types of dependences on the coefficient of variation of the distribution. By modeling the empirical formulas selected for analysis, a comparative analysis of their errors relative to accurate numerical solutions of the moment method equations was carried out. A renewed empirical formula for the shape parameter is proposed. An approach to estimating the scale parameter is proposed, in which the empirical formula of the latter is reduced to the product of the standard deviation of the distribution by a power function of the coefficient of variation with an exponent equal to – 1.027. The results of applying the updated empirical formulas to numerical data obtained by modeling a random sample from the Weibull distribution are presented. It is shown that the accuracy of the proposed empirical formulas is quite high.
Ключевые слова:
Weibull distribution, shape parameter, scale parameter, coefficient of variation, empirical formula, accuracy.
Citation:
Asatryan DG. Renewed empirical formulas of Weibull distribution parameters estimates. Computer Optics 2025; 49(1): 121-124. DOI: 10.18287/2412-6179-CO-1475.
References:
- Vega-Zuñiga S, Rueda-Bayona JG, Ospino-Castro A. Evaluation of eleven numerical methods for determining Weibull parameters for wind energy generation in the Caribbean region of Colombia. Math Model Eng Probl 2022; 9(1): 194-199. DOI: 10.18280/mmep.090124.
- Kapen PT, Gouajio MJ, Yemélé D. Analysis and efficient comparison of ten numerical methods inestimating Weibull parameters for wind energy potential: Application to the city of Bafoussam, Cameroon. Renew Energy 2020; 159: 1188-1198. DOI: 10.1016/j.renene.2020.05.185.
- Guenoukpati A, Salami AA, Kodjo MK, Napo K. Estimating Weibull parameters for wind energy applications using seven numerical methods: Casestudies of three coastal sites in West Africa. Int J Renew Energy Dev 2020; 9(2): 217-226. DOI: 10.14710/ijred.9.2.217-226.
- Justus CG, Hargraves WR, Mikhail A, Graber D. Methods for estimating wind speed frequency distributions. J Appl Meteorol Clim 1978; 17(3): 350-353. DOI: 10.1175/1520-0450(1978)017<0350:MFEWSF>2.0.CO;2.
- Ramírez PJ, Carta A. Influence of the data sampling interval in the estimation of parameters of the Weibull wind speed probability density distribution a case study. Energy Conv Manag 2005; 46: 2419-2438. DOI: 10.1016/J.ENCONMAN.2004.11.004.
- Mohammadi K, Mostafaeipour A. Using different methods for comprehensive study of wind turbine utilization in Zarrineh, Iran. Energy Conv Manag 2013; 65: 463-470. DOI: 10.1016/J.ENCONMAN.2012.09.004.
- Costa Rocha PA, Sousa RC, Andrade CF, Silva MEV. Comparison of seven numerical methods for determining Weibull parameters for wind energy generation in the northeast region of Brazil. Appl Energy 2012; 89: 395-400. DOI: 10.1016/j.apenergy.2011.08.003.
- Indhumathy D, Seshaiah CV, Sukkiramathi K. Estimation of Weibull parameters for wind speed calculation at Kanyakumari in India. Int J Innov Res Sci Eng Technol 2014; 3(1): 8341-8345.
- Mohammadi K, Alavi O, Mostafaeipour A, Goudarzi N, Jalilvand M. Assessing different parameters estimation methods of Weibull distribution to compute wind power density. Energy Conv Manag 2016; 108: 322-335. DOI: 10.1016/j.enconman.2015.11.015.
- Kelly M, Troen I, Jørgensen HE. Weibull-k revisited: "Tall" profiles and height variation of wind statistics. Boundary-Layer Meteorol 2014; 152(1): 107-124. DOI: 10.1007/s10546-014-9915-5.
- Robinson EY. Estimating Weibull parameters for materials. JPL Tech Memo 33-580. Pasadena, CA, USA: Jet Propulsion Lab; 1972. 62 p.
- Kanji O. A simple estimation method of Weibull modulus and verification with strength data. Appl Sci 2019; 9: 1575. DOI: 10.3390/app9081575.
- Azad AK, Rasul MG, Alam MM, Ameer Uddin SM, Sukanta Kumar M. Analysis of wind energy conversion system using Weibull distribution. Procedia Eng 2014; 90: 725-732. DOI: 10.1016/j.proeng.2014.11.803.
- Chang TP. Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application. Appl Energy 2011; 88(1): 272-282. DOI: 10.1016/j.apenergy.2010.06.018.
- Abramowitz M, Stegun IA, eds. Handbook of mathematical functions with formulas, graphs and mathematical tables. National Bureau of Standards; 1972. 1060 p.
- Asatryan DG. Comparative study of three approaches for estimating the Weibull distribution parameters. Vestnik RAU 2018; 2: 5-16.
- Asatryan DG. Gradient-based technique for image structural analysis and applications. Computer Optics 2019; 43(2): 245-250. DOI: 10.18287/2412-6179-2019-43-2-245-250.
© 2009, IPSI RAS
Россия, 443001, Самара, ул. Молодогвардейская, 151; электронная почта: journal@computeroptics.ru; тел: +7 (846) 242-41-24 (ответственный секретарь), +7 (846) 332-56-22 (технический редактор), факс: +7 (846) 332-56-20