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

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), 2021. 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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Cite This Article
  • 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
  • Department of Statistics, Ogun State Institute of Technology, Igbesa, Nigeria

  • Department of Mathematics and Statistics, Delta State Polytechnic, Ozoro, Nigeria

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

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