Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters

Okumu Otieno Kevin; Troon John Benedict; Samuel Muthiga Nganga

doi:doi:10.11648/j.ajtas.20221106.13

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Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters

Okumu Otieno Kevin, Troon John Benedict, Samuel Muthiga Nganga

Published in American Journal of Theoretical and Applied Statistics (Volume 11, Issue 6)

Received: 17 May 2022 Accepted: 16 June 2022 Published: 22 November 2022

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Abstract

Wind distributions are essential in making predictions on chances of getting particular wind speeds and even the ability of particular areas producing specified wind power. However, the accuracy of the parameters in predicting the wind speeds and potential wind power depends on the robustness of the distribution parameters in the fitted wind distribution model. The robustness of the parameter however depends on the estimation technique employed in the estimation of the distribution parameters. Past studies have shown that various researchers have used methods such as Maximum Likelihood Estimation (MLE), Minimum Distance Estimation (MDE) methods and other methods such as Method of Moments and Least Square Estimation technique. Despite this, the studies have not been able to compare the efficiency of the techniques estimating parameters for wind distributions to determine which of the technique is more efficient. The study aimed at determining the most efficient method in estimating the distribution parameters for wind speed using the hourly wind data for Narok County in Kenya, from January 2016 to December 2018. The study fitted both 2 parameter and 3 parameter distributions for wind in the region using the two techniques and then compared the relative efficiency of the estimated parameters. The results showed that both 2 and 3 parameter distributions fitted using the Maximum Likelihood Estimation (MLE) technique had smaller relative efficiency compare to those of Minimum Distance Estimation (MDE) technique. In conclusion, the results were able to determine that MLE gave out more efficient parameters for wind distribution than the MDE technique. The study therefore, recommended the use of MLE technique in estimating the parameters of wind distributions.

Published in	American Journal of Theoretical and Applied Statistics (Volume 11, Issue 6)
DOI	10.11648/j.ajtas.20221106.13
Page(s)	184-199
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Maximum Likelihood Estimation, Minimum Distance Estimation, Weibull, Gamma, Lognormal, AIC, BIC

References

[1]	Anderson, T. W., and Darling, D. A., (1952). Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. The Annals of mathematical statistics. Vol. 23, pp 193-212.
[2]	Akyuz, E., and Gamgam, H., (2017). Statistical analysis of wind speed data with Weibull and gamma distributions.
[3]	Ayodele, R., Adisa, A., Munda, L., and Agee, T., (2012). Statistical analysis of wind speed and wind power potential of Port Elizabeth using Weibull parameters. Tshwane University of technology, Pretoria, South Africa.
[4]	Azami, Z., Khadijah, S., Mahir, A., and Sopian, K., (2009). Wind speed analysis in east coast of Malaysia. European journal of scientific research. Vol. 2.
[5]	Celik, H., and Yilmaz, V., (2008). A statistical approach to estimate the wind speed distribution: the case study of Gelubolu region. Pp 122-132.
[6]	Dookie, I., Rocke, S., Singh, A., and Craig, J. R. (2018). Evaluating wind speed probability distribution models with novel goodness of fit metric: A Trinidad and Tobacco case study. International journal of energy and environmental engineering. 7, 33-59.
[7]	Galvao, F. A., and Wang, L., (2015). Efficient minimum distance estimator for quantile regression fixed effects panel data: Journal of multivariate analysis. 16, 211-243. DOI: 10.1093/jjfinec/nbx016.
[8]	Gungor A. and Eskin, N., (2008). The characteristics that defined wind as an energy source.
[9]	Gupta, R., and Biswas, A., (2010). Wind data analysis of Silchar (Assam India) by Rayleigh and Weibull methods. Journal of mechanical engineering research. Vol. 2, pp 10-24.
[10]	Hurlin, C., (2013). Maximum likelihood estimation. Advanced econometrics. University of Orleans.
[11]	Johnson, W., Donna, V., and Smith, L., (2010). Comparison of estimators for parameters of gamma distributions with left-truncated samples.
[12]	Lawan, S. M., Abidin, W. A. W. Z., Chai, W. Y., Baharum, A., and Masri, T., (2015). Statistical modelling of long-term wind speed data: American journal of computer science and information technology. 13, 79-121.
[13]	Maleki, F., and Deiri, E., (2007). Methods of estimation for three parameter reflected Weibull distribution.
[14]	Mert, I., and Karakus, C., (2015). A statistical analysis of wind speed using Burr, generalized gamma, and Weibull distribution in Antakya, Turkey. Turkish journal of electrical engineering and computer science.
[15]	Mumford, A. D., (1997). Robust parameter estimation for mixed Weibull (Seven parameters) including the method of maximum likelihood and the method of minimum distance: Department of air force, Air force institute of technology. DOI: 10.13140/RG.2.1.2868.6566.
[16]	Otieno, C. S., (2011). Analysis of wind speed based on Weibull model and data correlation for wind pattern description for a selected site in Juja, Kenya.
[17]	Oludhe, C., (1987). Statistical characteristics of wind power in Kenya. University of Nairobi.
[18]	Rahayu, A., Purhadi., Sutikno., and Prastyo, D. D., (2020). Multivariate gamma regression: parameter estimation, hypothesis testing, and its applications.
[19]	Rambachan, A., (2018). Maximum likelihood estimates and Minimum distance estimate.
[20]	Saleh, H., Abou, A. S., and Abdel-Hady, S., (2012). Assessment of different methods used to estimate Weibull distribution parameters for wind speeds in Zafarana wind farm, Suez gulf, Egypt.
[21]	Salma, O. B., and Abdelali A. E., (2018). Comparing maximum likelihood, least square and method of moments for Tas distribution: Journal of Humanities and Applies science. 11, 1-19.
[22]	Sanku, D., Menezes, A. F. B., and Mazucheli, J., (2019). Comparison of estimation methods for unit-Gamma distribution. Journal of data science. Vol. 17. pp 768-801.
[23]	Sultan, M. M. A., (2008). A data driven parameter estimation for the three parameter Weibull population from censored samples: Mathematical and computational applications. 13, 129-136.
[24]	Sukkiramathi, K., Seshaiah, C., and Indhumathy, D., (2014). A study of Weibull distribution to analyze the wind speed at Jogimatti in India. Vol. 01. pp 189-193.
[25]	Ulgen, K., and Hepbasli, A., (2002). Determination of Weibull parameters for wind energy analysis of Izmir, Turkey.
[26]	Ulgen, K., Genc, A., Hepbasli, A., and Oturanc, G., (2009). Assessment of wind characteristics for energy generation.
[27]	Woodward, A. W., William, R. S., Lindsey, H., and Gray, H. L., (1982). Comparison of minimum distance and maximum likelihood technique for proportion estimation: Department of statistics, Southern Methodist University. Available at: https://www.tandfonline.com. 590-598.
[28]	Zheng, S., (2018). Maximum likelihood estimation. Statistical theory II.

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APA Style

Okumu Otieno Kevin, Troon John Benedict, Samuel Muthiga Nganga. (2022). Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters. American Journal of Theoretical and Applied Statistics, 11(6), 184-199. https://doi.org/10.11648/j.ajtas.20221106.13

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ACS Style

Okumu Otieno Kevin; Troon John Benedict; Samuel Muthiga Nganga. Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters. Am. J. Theor. Appl. Stat. 2022, 11(6), 184-199. doi: 10.11648/j.ajtas.20221106.13

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AMA Style

Okumu Otieno Kevin, Troon John Benedict, Samuel Muthiga Nganga. Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters. Am J Theor Appl Stat. 2022;11(6):184-199. doi: 10.11648/j.ajtas.20221106.13

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@article{10.11648/j.ajtas.20221106.13,
  author = {Okumu Otieno Kevin and Troon John Benedict and Samuel Muthiga Nganga},
  title = {Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {6},
  pages = {184-199},
  doi = {10.11648/j.ajtas.20221106.13},
  url = {https://doi.org/10.11648/j.ajtas.20221106.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221106.13},
  abstract = {Wind distributions are essential in making predictions on chances of getting particular wind speeds and even the ability of particular areas producing specified wind power. However, the accuracy of the parameters in predicting the wind speeds and potential wind power depends on the robustness of the distribution parameters in the fitted wind distribution model. The robustness of the parameter however depends on the estimation technique employed in the estimation of the distribution parameters. Past studies have shown that various researchers have used methods such as Maximum Likelihood Estimation (MLE), Minimum Distance Estimation (MDE) methods and other methods such as Method of Moments and Least Square Estimation technique. Despite this, the studies have not been able to compare the efficiency of the techniques estimating parameters for wind distributions to determine which of the technique is more efficient. The study aimed at determining the most efficient method in estimating the distribution parameters for wind speed using the hourly wind data for Narok County in Kenya, from January 2016 to December 2018. The study fitted both 2 parameter and 3 parameter distributions for wind in the region using the two techniques and then compared the relative efficiency of the estimated parameters. The results showed that both 2 and 3 parameter distributions fitted using the Maximum Likelihood Estimation (MLE) technique had smaller relative efficiency compare to those of Minimum Distance Estimation (MDE) technique. In conclusion, the results were able to determine that MLE gave out more efficient parameters for wind distribution than the MDE technique. The study therefore, recommended the use of MLE technique in estimating the parameters of wind distributions.},
 year = {2022}
}

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TY  - JOUR
T1  - Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters
AU  - Okumu Otieno Kevin
AU  - Troon John Benedict
AU  - Samuel Muthiga Nganga
Y1  - 2022/11/22
PY  - 2022
N1  - https://doi.org/10.11648/j.ajtas.20221106.13
DO  - 10.11648/j.ajtas.20221106.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 184
EP  - 199
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20221106.13
AB  - Wind distributions are essential in making predictions on chances of getting particular wind speeds and even the ability of particular areas producing specified wind power. However, the accuracy of the parameters in predicting the wind speeds and potential wind power depends on the robustness of the distribution parameters in the fitted wind distribution model. The robustness of the parameter however depends on the estimation technique employed in the estimation of the distribution parameters. Past studies have shown that various researchers have used methods such as Maximum Likelihood Estimation (MLE), Minimum Distance Estimation (MDE) methods and other methods such as Method of Moments and Least Square Estimation technique. Despite this, the studies have not been able to compare the efficiency of the techniques estimating parameters for wind distributions to determine which of the technique is more efficient. The study aimed at determining the most efficient method in estimating the distribution parameters for wind speed using the hourly wind data for Narok County in Kenya, from January 2016 to December 2018. The study fitted both 2 parameter and 3 parameter distributions for wind in the region using the two techniques and then compared the relative efficiency of the estimated parameters. The results showed that both 2 and 3 parameter distributions fitted using the Maximum Likelihood Estimation (MLE) technique had smaller relative efficiency compare to those of Minimum Distance Estimation (MDE) technique. In conclusion, the results were able to determine that MLE gave out more efficient parameters for wind distribution than the MDE technique. The study therefore, recommended the use of MLE technique in estimating the parameters of wind distributions.
VL  - 11
IS  - 6
ER  -

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Author Information

Okumu Otieno Kevin

Department of Mathematics and Physical Sciences, Maasai Mara University, Narok, Kenya
Troon John Benedict

Department of Economics, Maasai Mara University, Narok, Kenya
Samuel Muthiga Nganga

Department of Mathematics and Physical Sciences, Maasai Mara University, Narok, Kenya

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APA Style

Okumu Otieno Kevin, Troon John Benedict, Samuel Muthiga Nganga. (2022). Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters. American Journal of Theoretical and Applied Statistics, 11(6), 184-199. https://doi.org/10.11648/j.ajtas.20221106.13

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ACS Style

Okumu Otieno Kevin; Troon John Benedict; Samuel Muthiga Nganga. Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters. Am. J. Theor. Appl. Stat. 2022, 11(6), 184-199. doi: 10.11648/j.ajtas.20221106.13

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AMA Style

Okumu Otieno Kevin, Troon John Benedict, Samuel Muthiga Nganga. Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters. Am J Theor Appl Stat. 2022;11(6):184-199. doi: 10.11648/j.ajtas.20221106.13

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@article{10.11648/j.ajtas.20221106.13,
  author = {Okumu Otieno Kevin and Troon John Benedict and Samuel Muthiga Nganga},
  title = {Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {6},
  pages = {184-199},
  doi = {10.11648/j.ajtas.20221106.13},
  url = {https://doi.org/10.11648/j.ajtas.20221106.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221106.13},
  abstract = {Wind distributions are essential in making predictions on chances of getting particular wind speeds and even the ability of particular areas producing specified wind power. However, the accuracy of the parameters in predicting the wind speeds and potential wind power depends on the robustness of the distribution parameters in the fitted wind distribution model. The robustness of the parameter however depends on the estimation technique employed in the estimation of the distribution parameters. Past studies have shown that various researchers have used methods such as Maximum Likelihood Estimation (MLE), Minimum Distance Estimation (MDE) methods and other methods such as Method of Moments and Least Square Estimation technique. Despite this, the studies have not been able to compare the efficiency of the techniques estimating parameters for wind distributions to determine which of the technique is more efficient. The study aimed at determining the most efficient method in estimating the distribution parameters for wind speed using the hourly wind data for Narok County in Kenya, from January 2016 to December 2018. The study fitted both 2 parameter and 3 parameter distributions for wind in the region using the two techniques and then compared the relative efficiency of the estimated parameters. The results showed that both 2 and 3 parameter distributions fitted using the Maximum Likelihood Estimation (MLE) technique had smaller relative efficiency compare to those of Minimum Distance Estimation (MDE) technique. In conclusion, the results were able to determine that MLE gave out more efficient parameters for wind distribution than the MDE technique. The study therefore, recommended the use of MLE technique in estimating the parameters of wind distributions.},
 year = {2022}
}

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TY  - JOUR
T1  - Comparative Analysis of Efficiency of Maximum Likelihood and Minimum Distance Estimation Techniques in Estimating Wind Distribution Parameters
AU  - Okumu Otieno Kevin
AU  - Troon John Benedict
AU  - Samuel Muthiga Nganga
Y1  - 2022/11/22
PY  - 2022
N1  - https://doi.org/10.11648/j.ajtas.20221106.13
DO  - 10.11648/j.ajtas.20221106.13
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 184
EP  - 199
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20221106.13
AB  - Wind distributions are essential in making predictions on chances of getting particular wind speeds and even the ability of particular areas producing specified wind power. However, the accuracy of the parameters in predicting the wind speeds and potential wind power depends on the robustness of the distribution parameters in the fitted wind distribution model. The robustness of the parameter however depends on the estimation technique employed in the estimation of the distribution parameters. Past studies have shown that various researchers have used methods such as Maximum Likelihood Estimation (MLE), Minimum Distance Estimation (MDE) methods and other methods such as Method of Moments and Least Square Estimation technique. Despite this, the studies have not been able to compare the efficiency of the techniques estimating parameters for wind distributions to determine which of the technique is more efficient. The study aimed at determining the most efficient method in estimating the distribution parameters for wind speed using the hourly wind data for Narok County in Kenya, from January 2016 to December 2018. The study fitted both 2 parameter and 3 parameter distributions for wind in the region using the two techniques and then compared the relative efficiency of the estimated parameters. The results showed that both 2 and 3 parameter distributions fitted using the Maximum Likelihood Estimation (MLE) technique had smaller relative efficiency compare to those of Minimum Distance Estimation (MDE) technique. In conclusion, the results were able to determine that MLE gave out more efficient parameters for wind distribution than the MDE technique. The study therefore, recommended the use of MLE technique in estimating the parameters of wind distributions.
VL  - 11
IS  - 6
ER  -

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