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

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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

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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), 2021. Published by Science Publishing Group

Keywords

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

References

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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

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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

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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

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@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}
}

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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  -

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

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

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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

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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

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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