The Least Square and the Weighted Least Square Methods for Estimating the Weibull Distribution Parameters - A Comparative Study

Pobocikova, Ivana; Michalková, Mária

doi:10.26552/com.c.2012.4.88-93

Cited by 6 publications

(4 citation statements)

References 6 publications

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“…( 18), defined by the graphical method, can be estimated by the LSM method as well. It is based on minimizing the Q(a,b) function when determining the regression parameters (Pobočíková & Sedliačková, 2012;Pobočíková et al, 2018).…”

Section: Least Square Methods (Lsm)mentioning

confidence: 99%

“…Similar to the LSM method, the regression parameters can be determined by minimizing Q(a,b) from Eq. ( 21) (Pobočíková & Sedliačková, 2012;Pobočíková et al, 2018).…”

Section: Weighted Least Squares Methods (Wlsm)mentioning

confidence: 99%

“…The evaluation of weight factors w i has been proposed by Bergman (1986) (Pobočíková & Sedliačková, 2012):…”

Section: Weighted Least Squares Methods (Wlsm)mentioning

confidence: 99%

“…Although the three-parameter Weibull distribution may give a more precise result when there is a high frequency of null winds speeds, the two-parameters Weibull distribution remains the most appropriate model and the most widely used in the wind industry sector provided the more accurate parameters are given (Justus & Mikhail, 1976;Kaoga et al, 2014;Kumar Pandey et al, 2020;Ulrich et al, 2018;Wais, 2017;Zhu, 2020). This aim of this paper is to analyse the accuracy in the determination of the two-parameters Weibull function namely shape parameter k and scale parameter c. Several models for estimating these parameters (k; c) have been developed, studied and even compared with each other (Akdağ & Dinler, 2009;Akgül et al, 2016;Andrade et al, 2014;Aukitino et al, 2017;Chang, 2011;Costa Rocha et al, 2012;Katinas et al, 2018;Li et al, 2020;Mohammadi et al, 2016;Mohammadi et al, 2017;Pobočíková & Sedliačková, 2012;Pobočíková et al, 2018;Wang et al, 2016;Werapun et al, 2015). Akdag et al demonstrated that his new power density method for calculating k and c parameters is more suitable than the maximum likelihood method and graphical method using 3 years of data from sites in Turkey (Akdağ & Dinler, 2009).…”

Section: Introductionmentioning

confidence: 99%

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Influence of Weibull parameters on the estimation of wind energy potential

Aziz

Tsuanyo

Nsouandele

et al. 2023

Sustainable Energy res.

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Wind potential estimation is generally evaluated using two-parameter (k, c) Weibull distribution. Root Mean Square Error (RMSE), Coefficient of Determination (R2) and Relative Error (RE) are computed in order to comparatively analyse fourteen methods of determining Weibull parameters. They are the Graphical Method, the Standard Deviation Method, the Empirical Method of Justus, the Empirical Method of Lysen, the Energy Pattern Factor Method, the Maximum Likelihood Method, the Modified Maximum Likelihood Method, the Alternative Maximum Likelihood Method, the Least Square Method, the Weighted Least squares Method, the Curve Fitting Method, the Wind Variability Method, the Moroccan Method and the Median and Quartile Method. These methods have been applied on three different windy sites (slightly, moderately and very windy sites) with hourly wind data over a period of 10 years (2005–2014), measured at 10 m height. As a result, compared to the other methods, Energy Pattern Factor method is the more suitable method applicable to assess the Weibull parameters for all wind speeds. However, the values obtained from RMSE, R2 and RE tests revealed that the WVM and MoroM methods are not suitable while all other methods are acceptable for the estimation of k and c. parameters. The determination of the wind power density and the gap between the predicted standard deviation by each method and the measured standard deviation for all the sites highlighted the relevance of EPFM method and the others methods. Moreover, this work reveals that the Weibull shape factor k decrease with height above ground level, while that of the scale factor c increase with height.

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Section: Least Square Methods (Lsm)mentioning

confidence: 99%

“…Similar to the LSM method, the regression parameters can be determined by minimizing Q(a,b) from Eq. ( 21) (Pobočíková & Sedliačková, 2012;Pobočíková et al, 2018).…”

Section: Weighted Least Squares Methods (Wlsm)mentioning

confidence: 99%

“…The evaluation of weight factors w i has been proposed by Bergman (1986) (Pobočíková & Sedliačková, 2012):…”

Section: Weighted Least Squares Methods (Wlsm)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Influence of Weibull parameters on the estimation of wind energy potential

Aziz

Tsuanyo

Nsouandele

et al. 2023

Sustainable Energy res.

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Comparison of mechanical and fatigue properties of SiMo- and SiCu-types of nodular cast iron

Vaško

2020

Materials Today: Proceedings

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Comparison of four methods for estimating the Weibull distribution parameters

Pobocikova¹,

Michalková²

2014

ams

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In this paper we study the performance of the least square method, the weighted least square method, the maximum likelihood method and the method of moments for estimating the Weibull distribution parameters. The comparison is based on the Monte Carlo simulation, the methods are compared in terms of the root mean square error and sample size n. The comparison shows that the maximum likelihood method and the method of moments provide similar estimates. We recommend the maximum likelihood method to estimate the Weibull distribution parameters due to its good properties. For very small sample sizes we recommend the weighted least square method.

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The Least Square and the Weighted Least Square Methods for Estimating the Weibull Distribution Parameters - A Comparative Study

Cited by 6 publications

References 6 publications

Influence of Weibull parameters on the estimation of wind energy potential

Influence of Weibull parameters on the estimation of wind energy potential

Comparison of mechanical and fatigue properties of SiMo- and SiCu-types of nodular cast iron

Comparison of four methods for estimating the Weibull distribution parameters

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