On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data

Obanla Olakunle James; Awariefe Christopher; Ilo Hammed Owolabi

doi:doi:10.11648/j.dmath.20210602.13

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On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data

Obanla Olakunle James, Awariefe Christopher, Ilo Hammed Owolabi

Published in International Journal of Discrete Mathematics (Volume 6, Issue 2)

Received: 29 May 2021 Accepted: 12 July 2021 Published: 23 November 2021

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Abstract

The focus of this paper is to estimate parameters of the best distribution for modelling wind speed data, real-life data sets of wind speed of Maiduguri, the biggest city in the North Eastern, Nigeria were adopted for application purposes. Six (6) probability density functions, specifically, Weibull, Gamma, Lognormal, Pareto, Burr and Log-Logistic are considered for modelling the wind speed data. In selecting the model of best fit for the variability of the wind speed data, five (5) methods of estimating parameter, such as; Maximum Likelihood Estimation (MLE), Matching Quantiles Estimation (MQE), The Cramer-von Mises Minimum Distance Estimators (CvM), Anderson-Darling Minimum Distance Estimation and Kolmogorov-Smirnov Minimum Distance Estimation (K-S)) were further applied to obtain the best estimates for the best model among compared ones. We discovered in our investigation that Weibull distribution best fitted the wind data per Goodness-of-fit tests, since it has the smallest p-value for K-S (0.03179314), CvM (0.03137888) and AD (0.23725978) revealing the curve is fairly close to our data and the maximum likelihood estimators with the smallest AIC (972.7990) and BIC (980.3105) estimates for Weibull parameters, proved to be the best as compared with other methods of estimation.

Published in	International Journal of Discrete Mathematics (Volume 6, Issue 2)
DOI	10.11648/j.dmath.20210602.13
Page(s)	45-51
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

Wind Energy, Probability Distribution Models, Maximum Likelihood Estimators, Matching Quantiles Estimation, Goodness of Fit-Tests

References

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APA Style

Obanla Olakunle James, Awariefe Christopher, Ilo Hammed Owolabi. (2021). On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data. International Journal of Discrete Mathematics, 6(2), 45-51. https://doi.org/10.11648/j.dmath.20210602.13

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ACS Style

Obanla Olakunle James; Awariefe Christopher; Ilo Hammed Owolabi. On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data. Int. J. Discrete Math. 2021, 6(2), 45-51. doi: 10.11648/j.dmath.20210602.13

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AMA Style

Obanla Olakunle James, Awariefe Christopher, Ilo Hammed Owolabi. On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data. Int J Discrete Math. 2021;6(2):45-51. doi: 10.11648/j.dmath.20210602.13

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@article{10.11648/j.dmath.20210602.13,
  author = {Obanla Olakunle James and Awariefe Christopher and Ilo Hammed Owolabi},
  title = {On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data},
  journal = {International Journal of Discrete Mathematics},
  volume = {6},
  number = {2},
  pages = {45-51},
  doi = {10.11648/j.dmath.20210602.13},
  url = {https://doi.org/10.11648/j.dmath.20210602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20210602.13},
  abstract = {The focus of this paper is to estimate parameters of the best distribution for modelling wind speed data, real-life data sets of wind speed of Maiduguri, the biggest city in the North Eastern, Nigeria were adopted for application purposes. Six (6) probability density functions, specifically, Weibull, Gamma, Lognormal, Pareto, Burr and Log-Logistic are considered for modelling the wind speed data. In selecting the model of best fit for the variability of the wind speed data, five (5) methods of estimating parameter, such as; Maximum Likelihood Estimation (MLE), Matching Quantiles Estimation (MQE), The Cramer-von Mises Minimum Distance Estimators (CvM), Anderson-Darling Minimum Distance Estimation and Kolmogorov-Smirnov Minimum Distance Estimation (K-S)) were further applied to obtain the best estimates for the best model among compared ones. We discovered in our investigation that Weibull distribution best fitted the wind data per Goodness-of-fit tests, since it has the smallest p-value for K-S (0.03179314), CvM (0.03137888) and AD (0.23725978) revealing the curve is fairly close to our data and the maximum likelihood estimators with the smallest AIC (972.7990) and BIC (980.3105) estimates for Weibull parameters, proved to be the best as compared with other methods of estimation.},
 year = {2021}
}

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TY  - JOUR
T1  - On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data
AU  - Obanla Olakunle James
AU  - Awariefe Christopher
AU  - Ilo Hammed Owolabi
Y1  - 2021/11/23
PY  - 2021
N1  - https://doi.org/10.11648/j.dmath.20210602.13
DO  - 10.11648/j.dmath.20210602.13
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 45
EP  - 51
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20210602.13
AB  - The focus of this paper is to estimate parameters of the best distribution for modelling wind speed data, real-life data sets of wind speed of Maiduguri, the biggest city in the North Eastern, Nigeria were adopted for application purposes. Six (6) probability density functions, specifically, Weibull, Gamma, Lognormal, Pareto, Burr and Log-Logistic are considered for modelling the wind speed data. In selecting the model of best fit for the variability of the wind speed data, five (5) methods of estimating parameter, such as; Maximum Likelihood Estimation (MLE), Matching Quantiles Estimation (MQE), The Cramer-von Mises Minimum Distance Estimators (CvM), Anderson-Darling Minimum Distance Estimation and Kolmogorov-Smirnov Minimum Distance Estimation (K-S)) were further applied to obtain the best estimates for the best model among compared ones. We discovered in our investigation that Weibull distribution best fitted the wind data per Goodness-of-fit tests, since it has the smallest p-value for K-S (0.03179314), CvM (0.03137888) and AD (0.23725978) revealing the curve is fairly close to our data and the maximum likelihood estimators with the smallest AIC (972.7990) and BIC (980.3105) estimates for Weibull parameters, proved to be the best as compared with other methods of estimation.
VL  - 6
IS  - 2
ER  -

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Author Information

Obanla Olakunle James

Department of Statistics, Ogun State Institute of Technology, Igbesa, Nigeria
Awariefe Christopher

Department of Mathematics and Statistics, Delta State Polytechnic, Ozoro, Nigeria
Ilo Hammed Owolabi

Department of Statistics, Ogun State Institute of Technology, Igbesa, Nigeria

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APA Style

Obanla Olakunle James, Awariefe Christopher, Ilo Hammed Owolabi. (2021). On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data. International Journal of Discrete Mathematics, 6(2), 45-51. https://doi.org/10.11648/j.dmath.20210602.13

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ACS Style

Obanla Olakunle James; Awariefe Christopher; Ilo Hammed Owolabi. On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data. Int. J. Discrete Math. 2021, 6(2), 45-51. doi: 10.11648/j.dmath.20210602.13

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AMA Style

Obanla Olakunle James, Awariefe Christopher, Ilo Hammed Owolabi. On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data. Int J Discrete Math. 2021;6(2):45-51. doi: 10.11648/j.dmath.20210602.13

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@article{10.11648/j.dmath.20210602.13,
  author = {Obanla Olakunle James and Awariefe Christopher and Ilo Hammed Owolabi},
  title = {On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data},
  journal = {International Journal of Discrete Mathematics},
  volume = {6},
  number = {2},
  pages = {45-51},
  doi = {10.11648/j.dmath.20210602.13},
  url = {https://doi.org/10.11648/j.dmath.20210602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20210602.13},
  abstract = {The focus of this paper is to estimate parameters of the best distribution for modelling wind speed data, real-life data sets of wind speed of Maiduguri, the biggest city in the North Eastern, Nigeria were adopted for application purposes. Six (6) probability density functions, specifically, Weibull, Gamma, Lognormal, Pareto, Burr and Log-Logistic are considered for modelling the wind speed data. In selecting the model of best fit for the variability of the wind speed data, five (5) methods of estimating parameter, such as; Maximum Likelihood Estimation (MLE), Matching Quantiles Estimation (MQE), The Cramer-von Mises Minimum Distance Estimators (CvM), Anderson-Darling Minimum Distance Estimation and Kolmogorov-Smirnov Minimum Distance Estimation (K-S)) were further applied to obtain the best estimates for the best model among compared ones. We discovered in our investigation that Weibull distribution best fitted the wind data per Goodness-of-fit tests, since it has the smallest p-value for K-S (0.03179314), CvM (0.03137888) and AD (0.23725978) revealing the curve is fairly close to our data and the maximum likelihood estimators with the smallest AIC (972.7990) and BIC (980.3105) estimates for Weibull parameters, proved to be the best as compared with other methods of estimation.},
 year = {2021}
}

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TY  - JOUR
T1  - On the Investigation of the Methods of Parameter Estimation of the Best Probability Model for Wind Speed Data
AU  - Obanla Olakunle James
AU  - Awariefe Christopher
AU  - Ilo Hammed Owolabi
Y1  - 2021/11/23
PY  - 2021
N1  - https://doi.org/10.11648/j.dmath.20210602.13
DO  - 10.11648/j.dmath.20210602.13
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 45
EP  - 51
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20210602.13
AB  - The focus of this paper is to estimate parameters of the best distribution for modelling wind speed data, real-life data sets of wind speed of Maiduguri, the biggest city in the North Eastern, Nigeria were adopted for application purposes. Six (6) probability density functions, specifically, Weibull, Gamma, Lognormal, Pareto, Burr and Log-Logistic are considered for modelling the wind speed data. In selecting the model of best fit for the variability of the wind speed data, five (5) methods of estimating parameter, such as; Maximum Likelihood Estimation (MLE), Matching Quantiles Estimation (MQE), The Cramer-von Mises Minimum Distance Estimators (CvM), Anderson-Darling Minimum Distance Estimation and Kolmogorov-Smirnov Minimum Distance Estimation (K-S)) were further applied to obtain the best estimates for the best model among compared ones. We discovered in our investigation that Weibull distribution best fitted the wind data per Goodness-of-fit tests, since it has the smallest p-value for K-S (0.03179314), CvM (0.03137888) and AD (0.23725978) revealing the curve is fairly close to our data and the maximum likelihood estimators with the smallest AIC (972.7990) and BIC (980.3105) estimates for Weibull parameters, proved to be the best as compared with other methods of estimation.
VL  - 6
IS  - 2
ER  -

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