Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method

Okumu Otieno Kevin; Edgar Otumba; Alilah Anekeya David; John Matuya

doi:doi:10.11648/j.ijsd.20200603.13

| Peer-Reviewed

Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method

Okumu Otieno Kevin, Edgar Otumba, Alilah Anekeya David, John Matuya

Published in International Journal of Statistical Distributions and Applications (Volume 6, Issue 3)

Received: 13 September 2020 Accepted: 27 September 2020 Published: 13 October 2020

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Kenya is among the countries that are continuously investing in wind energy to meet her electricity demand. Kenya is working towards its vision 2030 of achieving a total of 2GW of energy from wind industry. To achieve this, there is a need that all the relevant data on wind characteristics must be available. The purpose of this study is, therefore, to find the most efficient two-parameter model for fitting wind speed distribution for Narok County in Kenya, using the maximum likelihood method. Hourly wind speed data collected for a period of three years (2016 to 2018) from five sites within Narok County was used. Each of the distribution’s parameters was estimated and then a suitability test of the parameters was conducted using the goodness of fit test statistics, Kolmogorov-Smirnov, and Anderson-Darling. An efficiency test was determined using the Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values, with the best decision taken based on the distribution having a smaller value of AIC and BIC. The results showed that the best distributions were the gamma distribution with the shape parameter of 2.47634 and scale parameter of 1.25991, implying that gamma distribution was the best distribution for modeling Narok County wind speed data.

Published in	International Journal of Statistical Distributions and Applications (Volume 6, Issue 3)
DOI	10.11648/j.ijsd.20200603.13
Page(s)	57-64
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

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 on 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 the 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]	Hurlin, C., (2013). Maximum likelihood estimation. Advanced econometrics. The University of Orleans.
[10]	Johnson, W., Donna, V., and Smith, L., (2010). Comparison of estimators for parameters of gamma distributions with left-truncated samples.
[11]	Maleki, F., and Deiri, E., (2007). Methods of estimation for three-parameter reflected Weibull distribution.
[12]	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.
[13]	Oludhe, C., (1987). Statistical characteristics of wind power in Kenya. The University of Nairobi.
[14]	Rahayu, A., Purhadi., Sutikno., and Prastyo, D. D., (2020). Multivariate gamma regression: parameter estimation, hypothesis testing, and applications.
[15]	Rambachan, A., (2018). Maximum likelihood estimates and Minimum distance estimate.
[16]	Solar and wind energy resource assessment. (2008). Kenya country report.
[17]	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.
[18]	Ulgen, K., and Hepbasli, A., (2002). Determination of Weibull parameters for wind energy analysis of Izmir, Turkey.
[19]	Ulgen, K., Genc, A., Hepbasli, A., and Oturanc, G., (2009). Assessment of wind characteristics for energy generation.
[20]	Wind sector prospectus Kenya. (2013). Wind energy data analysis and development program.
[21]	Zheng, S., (2018). Maximum likelihood estimation. Statistical theory II.

Cite This Article

Plain Text BibTeX RIS

APA Style

Okumu Otieno Kevin, Edgar Otumba, Alilah Anekeya David, John Matuya. (2020). Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method. International Journal of Statistical Distributions and Applications, 6(3), 57-64. https://doi.org/10.11648/j.ijsd.20200603.13

Copy | Download

ACS Style

Okumu Otieno Kevin; Edgar Otumba; Alilah Anekeya David; John Matuya. Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method. Int. J. Stat. Distrib. Appl. 2020, 6(3), 57-64. doi: 10.11648/j.ijsd.20200603.13

Copy | Download

AMA Style

Okumu Otieno Kevin, Edgar Otumba, Alilah Anekeya David, John Matuya. Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method. Int J Stat Distrib Appl. 2020;6(3):57-64. doi: 10.11648/j.ijsd.20200603.13

Copy | Download

@article{10.11648/j.ijsd.20200603.13,
  author = {Okumu Otieno Kevin and Edgar Otumba and Alilah Anekeya David and John Matuya},
  title = {Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {6},
  number = {3},
  pages = {57-64},
  doi = {10.11648/j.ijsd.20200603.13},
  url = {https://doi.org/10.11648/j.ijsd.20200603.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20200603.13},
  abstract = {Kenya is among the countries that are continuously investing in wind energy to meet her electricity demand. Kenya is working towards its vision 2030 of achieving a total of 2GW of energy from wind industry. To achieve this, there is a need that all the relevant data on wind characteristics must be available. The purpose of this study is, therefore, to find the most efficient two-parameter model for fitting wind speed distribution for Narok County in Kenya, using the maximum likelihood method. Hourly wind speed data collected for a period of three years (2016 to 2018) from five sites within Narok County was used. Each of the distribution’s parameters was estimated and then a suitability test of the parameters was conducted using the goodness of fit test statistics, Kolmogorov-Smirnov, and Anderson-Darling. An efficiency test was determined using the Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values, with the best decision taken based on the distribution having a smaller value of AIC and BIC. The results showed that the best distributions were the gamma distribution with the shape parameter of 2.47634 and scale parameter of 1.25991, implying that gamma distribution was the best distribution for modeling Narok County wind speed data.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method
AU  - Okumu Otieno Kevin
AU  - Edgar Otumba
AU  - Alilah Anekeya David
AU  - John Matuya
Y1  - 2020/10/13
PY  - 2020
N1  - https://doi.org/10.11648/j.ijsd.20200603.13
DO  - 10.11648/j.ijsd.20200603.13
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  - 57
EP  - 64
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20200603.13
AB  - Kenya is among the countries that are continuously investing in wind energy to meet her electricity demand. Kenya is working towards its vision 2030 of achieving a total of 2GW of energy from wind industry. To achieve this, there is a need that all the relevant data on wind characteristics must be available. The purpose of this study is, therefore, to find the most efficient two-parameter model for fitting wind speed distribution for Narok County in Kenya, using the maximum likelihood method. Hourly wind speed data collected for a period of three years (2016 to 2018) from five sites within Narok County was used. Each of the distribution’s parameters was estimated and then a suitability test of the parameters was conducted using the goodness of fit test statistics, Kolmogorov-Smirnov, and Anderson-Darling. An efficiency test was determined using the Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values, with the best decision taken based on the distribution having a smaller value of AIC and BIC. The results showed that the best distributions were the gamma distribution with the shape parameter of 2.47634 and scale parameter of 1.25991, implying that gamma distribution was the best distribution for modeling Narok County wind speed data.
VL  - 6
IS  - 3
ER  -

Copy | Download

Author Information

Okumu Otieno Kevin

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

Department of Statistics and Actuarial Sciences, Maseno University, Kisumu, Kenya
Alilah Anekeya David

Department of Mathematics, Masinde Muliro University of Science and Technology, Kakamega, Kenya
John Matuya

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Okumu Otieno Kevin, Edgar Otumba, Alilah Anekeya David, John Matuya. (2020). Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method. International Journal of Statistical Distributions and Applications, 6(3), 57-64. https://doi.org/10.11648/j.ijsd.20200603.13

Copy | Download

ACS Style

Okumu Otieno Kevin; Edgar Otumba; Alilah Anekeya David; John Matuya. Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method. Int. J. Stat. Distrib. Appl. 2020, 6(3), 57-64. doi: 10.11648/j.ijsd.20200603.13

Copy | Download

AMA Style

Okumu Otieno Kevin, Edgar Otumba, Alilah Anekeya David, John Matuya. Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method. Int J Stat Distrib Appl. 2020;6(3):57-64. doi: 10.11648/j.ijsd.20200603.13

Copy | Download

@article{10.11648/j.ijsd.20200603.13,
  author = {Okumu Otieno Kevin and Edgar Otumba and Alilah Anekeya David and John Matuya},
  title = {Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {6},
  number = {3},
  pages = {57-64},
  doi = {10.11648/j.ijsd.20200603.13},
  url = {https://doi.org/10.11648/j.ijsd.20200603.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20200603.13},
  abstract = {Kenya is among the countries that are continuously investing in wind energy to meet her electricity demand. Kenya is working towards its vision 2030 of achieving a total of 2GW of energy from wind industry. To achieve this, there is a need that all the relevant data on wind characteristics must be available. The purpose of this study is, therefore, to find the most efficient two-parameter model for fitting wind speed distribution for Narok County in Kenya, using the maximum likelihood method. Hourly wind speed data collected for a period of three years (2016 to 2018) from five sites within Narok County was used. Each of the distribution’s parameters was estimated and then a suitability test of the parameters was conducted using the goodness of fit test statistics, Kolmogorov-Smirnov, and Anderson-Darling. An efficiency test was determined using the Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values, with the best decision taken based on the distribution having a smaller value of AIC and BIC. The results showed that the best distributions were the gamma distribution with the shape parameter of 2.47634 and scale parameter of 1.25991, implying that gamma distribution was the best distribution for modeling Narok County wind speed data.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Fitting Wind Speed to a Two Parameter Distribution Model Using Maximum Likelihood Estimation Method
AU  - Okumu Otieno Kevin
AU  - Edgar Otumba
AU  - Alilah Anekeya David
AU  - John Matuya
Y1  - 2020/10/13
PY  - 2020
N1  - https://doi.org/10.11648/j.ijsd.20200603.13
DO  - 10.11648/j.ijsd.20200603.13
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  - 57
EP  - 64
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20200603.13
AB  - Kenya is among the countries that are continuously investing in wind energy to meet her electricity demand. Kenya is working towards its vision 2030 of achieving a total of 2GW of energy from wind industry. To achieve this, there is a need that all the relevant data on wind characteristics must be available. The purpose of this study is, therefore, to find the most efficient two-parameter model for fitting wind speed distribution for Narok County in Kenya, using the maximum likelihood method. Hourly wind speed data collected for a period of three years (2016 to 2018) from five sites within Narok County was used. Each of the distribution’s parameters was estimated and then a suitability test of the parameters was conducted using the goodness of fit test statistics, Kolmogorov-Smirnov, and Anderson-Darling. An efficiency test was determined using the Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC) values, with the best decision taken based on the distribution having a smaller value of AIC and BIC. The results showed that the best distributions were the gamma distribution with the shape parameter of 2.47634 and scale parameter of 1.25991, implying that gamma distribution was the best distribution for modeling Narok County wind speed data.
VL  - 6
IS  - 3
ER  -

Copy | Download