Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique

Okumu Otieno Kevin; Troon John Benedict; Samuel Muthiga Ngaga

doi:doi:10.11648/j.ijsd.20210701.11

| Peer-Reviewed

Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique

Okumu Otieno Kevin, Troon John Benedict, Samuel Muthiga Ngaga

Published in International Journal of Statistical Distributions and Applications (Volume 7, Issue 1)

Received: 13 December 2020 Accepted: 30 December 2020 Published: 4 March 2021

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Kenya is one of the countries in the world with a good quantity of wind. This makes the country to work on technologies that can help in harnessing the wind with a vision of achieving a total capacity of 2GW of wind energy by 2030. The objective of this research is to find the best three-parameter wind speed distribution for examining wind speed using the maximum likelihood fitting technique. To achieve the objective, the study used hourly wind speed data collected for a period of three years (2016 – 2018) from five sites within Narok County. The study examines the best distributions that the data fits and then conducted a suitability test of the distributions using the Kolmogorov-Smirnov test. The distribution parameters were fitted using maximum likelihood technique and model comparison test conducted using Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values with the decision rule that the best distribution relies on the distribution with the smaller AIC and BIC values. The research showed that the best distribution is the gamma distribution with the shape parameter of 2.071773, scale parameter of 1.120855, and threshold parameter of 0.1174. A conclusion that gamma distribution is the best three-parameter distribution for examining the Narok country wind speed data.

Published in	International Journal of Statistical Distributions and Applications (Volume 7, Issue 1)
DOI	10.11648/j.ijsd.20210701.11
Page(s)	1-6
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), 2024. Published by Science Publishing Group

Keywords

Maximum Likelihood Estimation, Wind Speed, Weibull, Gamma, Lognormal, AIC, BIC

References

[1]	Akyuz, E., and Gamgam, H., (2017). Statistical analysis of wind speed data with Weibull and gamma distributions.
[2]	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.
[3]	Azami, Z., Khadijah, S., Mahir, A., and Sopian, K., (2009). Wind speed analysis in the east coast of Malaysia. European journal of scientific research. Vol. 2.
[4]	Barasa, M., (2013). Wind regime analysis and reserve estimation in Kenya.
[5]	Brenda, F. G., (2009). Parameter estimation for the lognormal distribution. Brigham Young University.
[6]	Celik, H., and Yilmaz, V., (2008). A statistical approach to estimate the wind speed distribution: the case study of Gelubolu region. Pp 122-132.
[7]	Chu, Y. K., and Ke, J. C., (2012). Computation approaches for parameter estimation of Weibull distribution. Mathematical and computational applications. Vol. 17. pp 39-47.
[8]	Gungor A. and Eskin, N., (2008). The characteristics that define 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. The 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]	Maleki, F., and Deiri, E., (2007). Methods of estimation for three-parameter reflected Weibull distribution.
[13]	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.
[14]	Oludhe, C., (1987). Statistical characteristics of wind power in Kenya. The University of Nairobi.
[15]	Rahayu, A., Purhadi., Sutikno., and Prastyo, D. D., (2020). Multivariate gamma regression: parameter estimation, hypothesis testing, and applications.
[16]	Rambachan, A., (2018). Maximum likelihood estimates and Minimum distance estimates.
[17]	Solar and wind energy resource assessment. (2008). Kenya country report.
[18]	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.
[19]	Ulgen, K., and Hepbasli, A., (2002). Determination of Weibull parameters for wind energy analysis of Izmir, Turkey.
[20]	Ulgen, K., Genc, A., Hepbasli, A., and Oturanc, G., (2009). Assessment of wind characteristics for energy generation.
[21]	Wind sector prospectus Kenya. (2013). Wind energy data analysis and development program.
[22]	Zheng, S., (2018). Maximum likelihood estimation. Statistical theory II.
[23]	Rigby, R. S., Mikis, H., Gillian, D., and Fernade. (2019). Maximum likelihood estimation. 10.1201/9780429298547-11.
[24]	Denuit, Michel & Hainaut, Donatien & Trufin, Julien. (2019). Maximum Likelihood Estimation. 10.1007/978-3-030-25820-7_3.
[25]	Magnus, Jan. (2019). Maximum likelihood estimation. 346-366. 10.1002/9781119541219.ch15.
[26]	Clement, Nadia & Lasky, Ronald. (2020). Weibull Distribution and Analysis: 2019. 1-5. 10.23919/PanPacific48324.2020.9059313.
[27]	Kizilersu, Ayse & Kreer, Markus & Thomas, Anthony. (2018). The Weibull distribution. Significance. 15. 10-11. 10.1111/j.1740-9713.2018.01123.x.
[28]	Dagpunar, John. (2019). The gamma distribution. Significance. 16. 10-11. 10.1111/j.1740-9713.2019.01226.x.
[29]	Hart, P. (2017). Lognormal Distribution. 10.1057/978-1-349-95121-5_1089-2.

Cite This Article

Plain Text BibTeX RIS

APA Style

Okumu Otieno Kevin, Troon John Benedict, Samuel Muthiga Ngaga. (2021). Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique. International Journal of Statistical Distributions and Applications, 7(1), 1-6. https://doi.org/10.11648/j.ijsd.20210701.11

Copy | Download

ACS Style

Okumu Otieno Kevin; Troon John Benedict; Samuel Muthiga Ngaga. Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique. Int. J. Stat. Distrib. Appl. 2021, 7(1), 1-6. doi: 10.11648/j.ijsd.20210701.11

Copy | Download

AMA Style

Okumu Otieno Kevin, Troon John Benedict, Samuel Muthiga Ngaga. Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique. Int J Stat Distrib Appl. 2021;7(1):1-6. doi: 10.11648/j.ijsd.20210701.11

Copy | Download

@article{10.11648/j.ijsd.20210701.11,
  author = {Okumu Otieno Kevin and Troon John Benedict and Samuel Muthiga Ngaga},
  title = {Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {7},
  number = {1},
  pages = {1-6},
  doi = {10.11648/j.ijsd.20210701.11},
  url = {https://doi.org/10.11648/j.ijsd.20210701.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20210701.11},
  abstract = {Kenya is one of the countries in the world with a good quantity of wind. This makes the country to work on technologies that can help in harnessing the wind with a vision of achieving a total capacity of 2GW of wind energy by 2030. The objective of this research is to find the best three-parameter wind speed distribution for examining wind speed using the maximum likelihood fitting technique. To achieve the objective, the study used hourly wind speed data collected for a period of three years (2016 – 2018) from five sites within Narok County. The study examines the best distributions that the data fits and then conducted a suitability test of the distributions using the Kolmogorov-Smirnov test. The distribution parameters were fitted using maximum likelihood technique and model comparison test conducted using Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values with the decision rule that the best distribution relies on the distribution with the smaller AIC and BIC values. The research showed that the best distribution is the gamma distribution with the shape parameter of 2.071773, scale parameter of 1.120855, and threshold parameter of 0.1174. A conclusion that gamma distribution is the best three-parameter distribution for examining the Narok country wind speed data.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique
AU  - Okumu Otieno Kevin
AU  - Troon John Benedict
AU  - Samuel Muthiga Ngaga
Y1  - 2021/03/04
PY  - 2021
N1  - https://doi.org/10.11648/j.ijsd.20210701.11
DO  - 10.11648/j.ijsd.20210701.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 1
EP  - 6
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20210701.11
AB  - Kenya is one of the countries in the world with a good quantity of wind. This makes the country to work on technologies that can help in harnessing the wind with a vision of achieving a total capacity of 2GW of wind energy by 2030. The objective of this research is to find the best three-parameter wind speed distribution for examining wind speed using the maximum likelihood fitting technique. To achieve the objective, the study used hourly wind speed data collected for a period of three years (2016 – 2018) from five sites within Narok County. The study examines the best distributions that the data fits and then conducted a suitability test of the distributions using the Kolmogorov-Smirnov test. The distribution parameters were fitted using maximum likelihood technique and model comparison test conducted using Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values with the decision rule that the best distribution relies on the distribution with the smaller AIC and BIC values. The research showed that the best distribution is the gamma distribution with the shape parameter of 2.071773, scale parameter of 1.120855, and threshold parameter of 0.1174. A conclusion that gamma distribution is the best three-parameter distribution for examining the Narok country wind speed data.
VL  - 7
IS  - 1
ER  -

Copy | Download

Author Information

Okumu Otieno Kevin

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

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

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Okumu Otieno Kevin, Troon John Benedict, Samuel Muthiga Ngaga. (2021). Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique. International Journal of Statistical Distributions and Applications, 7(1), 1-6. https://doi.org/10.11648/j.ijsd.20210701.11

Copy | Download

ACS Style

Okumu Otieno Kevin; Troon John Benedict; Samuel Muthiga Ngaga. Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique. Int. J. Stat. Distrib. Appl. 2021, 7(1), 1-6. doi: 10.11648/j.ijsd.20210701.11

Copy | Download

AMA Style

Okumu Otieno Kevin, Troon John Benedict, Samuel Muthiga Ngaga. Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique. Int J Stat Distrib Appl. 2021;7(1):1-6. doi: 10.11648/j.ijsd.20210701.11

Copy | Download

@article{10.11648/j.ijsd.20210701.11,
  author = {Okumu Otieno Kevin and Troon John Benedict and Samuel Muthiga Ngaga},
  title = {Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {7},
  number = {1},
  pages = {1-6},
  doi = {10.11648/j.ijsd.20210701.11},
  url = {https://doi.org/10.11648/j.ijsd.20210701.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20210701.11},
  abstract = {Kenya is one of the countries in the world with a good quantity of wind. This makes the country to work on technologies that can help in harnessing the wind with a vision of achieving a total capacity of 2GW of wind energy by 2030. The objective of this research is to find the best three-parameter wind speed distribution for examining wind speed using the maximum likelihood fitting technique. To achieve the objective, the study used hourly wind speed data collected for a period of three years (2016 – 2018) from five sites within Narok County. The study examines the best distributions that the data fits and then conducted a suitability test of the distributions using the Kolmogorov-Smirnov test. The distribution parameters were fitted using maximum likelihood technique and model comparison test conducted using Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values with the decision rule that the best distribution relies on the distribution with the smaller AIC and BIC values. The research showed that the best distribution is the gamma distribution with the shape parameter of 2.071773, scale parameter of 1.120855, and threshold parameter of 0.1174. A conclusion that gamma distribution is the best three-parameter distribution for examining the Narok country wind speed data.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Fitting Wind Speed to a 3-Parameter Distribution Using Maximum Likelihood Technique
AU  - Okumu Otieno Kevin
AU  - Troon John Benedict
AU  - Samuel Muthiga Ngaga
Y1  - 2021/03/04
PY  - 2021
N1  - https://doi.org/10.11648/j.ijsd.20210701.11
DO  - 10.11648/j.ijsd.20210701.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 1
EP  - 6
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20210701.11
AB  - Kenya is one of the countries in the world with a good quantity of wind. This makes the country to work on technologies that can help in harnessing the wind with a vision of achieving a total capacity of 2GW of wind energy by 2030. The objective of this research is to find the best three-parameter wind speed distribution for examining wind speed using the maximum likelihood fitting technique. To achieve the objective, the study used hourly wind speed data collected for a period of three years (2016 – 2018) from five sites within Narok County. The study examines the best distributions that the data fits and then conducted a suitability test of the distributions using the Kolmogorov-Smirnov test. The distribution parameters were fitted using maximum likelihood technique and model comparison test conducted using Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values with the decision rule that the best distribution relies on the distribution with the smaller AIC and BIC values. The research showed that the best distribution is the gamma distribution with the shape parameter of 2.071773, scale parameter of 1.120855, and threshold parameter of 0.1174. A conclusion that gamma distribution is the best three-parameter distribution for examining the Narok country wind speed data.
VL  - 7
IS  - 1
ER  -

Copy | Download