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

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.

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

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

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

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

Copyright © 2021 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Amaya-Martínez, P. A., Saavedra-Montes, A. J and Arango-Zuluaga, E. I. (2014). A statistical analysis of wind speed distribution models in the Aburrá Valley, Colombia. CT & F - Ciencia, Tecnología y Futuro, 5 (5), 121-136.
2. Amoroso, L. (1938). "VILFREDO PARETO". Econometrica (Pre-1986); Jan 1938; 6, 1; ProQuest.
3. Anderson, T. W., Darling, D. A. (1954). A Test of Goodness of Fit, Journal of American Statistics Association, pp. 765-767.
4. D’Agostino R, Stephens M. Goodness-of-fit Techniques, Marcel Dekker, New York, NY, USA.
5. Kaoga, D., Danwe, R., Doka, S and Djongyang, N. (2015) Statistical Analysis of Wind Speed Distribution based on six Weibull Methods for Wind Power evaluation in Garoua, Cameroon. Revue des Energies Renouvelables. 18. 105-125.
6. Lawless, J. F. (2003), Statistical Models and Methods for Lifetime Data, Second edition, Wiley, New York, pp. 168.
7. Li, M. & Li, X. (2005). MEP-type distribution function: a better alternative to Weibull function for wind speed distributions. Renew. Energy, 30 (8), 1221-1240.
8. Li, Z., Brissette, F. and Chen, J. (2013) Finding the most appropriate precipitation probability distribution for stochastic weather generation and hydrological modeling in Nordic watersheds. Hydrological Processes, vol. 27, no. 25, pp. 3718–3729.
9. Lilliefors, H. W (1967) On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, 62, 399-402.
10. Lo Brano, V., Orioli, A., Ciulla, G. & Culotta, S. (2011). Quality of wind speed fitting distributions for the urban area of Palermo, Italy. Renew. Energy, 36 (3), 1026-1039.
11. Louzada, F., Marchi, V and Carpenter, J. (2013). The complementary exponentiated exponential geometric lifetime distribution,” Journal of Probability and Statistics, vol. 2013, Article ID 502159, 10 pages.
12. Luceno A. (2006). Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators. Computational Statistics and Data Analysis, Vol. 51, no. 2, pp. 904-917.
13. Lun, I. Y. F., Lan J. C. (2000). A study of Weibull parameters using long-term wind observations. Renewable Energy, vol. 20, pp. 145–53.
14. Macdonald P. D. M. (1971). Comment on an estimation procedure for mixtures of distributions by Choi and Bulgeren, Journal of the Royal Statistical Society, Series B: Methodological. vol. 33, no. 2, pp. 326-329.
15. Moeschberger, M. L (1997). Survival Analysis. Secaucus, NJ, USA: Springer-Verlag New York, Inc.
16. Obanla, O. J., Awariefe, C and Afolabi, N. O. (2018). Comparative Study of Modeling Wind Speed Data: A Case Study of Maiduguri, Nigeria. International Journal of Research, 2348-795X, 05 (17).
17. Rahman, A. S., Rahman, A., Zaman, M. A., Haddad, K., Ahsan, A and Imteaz, M. (2013) A study on selection of probability distributions for at-site flood frequency analysis in Australia. Natural Hazards, vol. 69, no. 3, pp. 1803–1813.
18. Rasheed, Huda & Naji, Loaiy. (2019). Estimate the Two Parameters of Gamma Distribution Under Entropy Loss Function. Iraqi Journal of Science. 60. 127-134. 10.24996/ijs.2019.60.1.14.
19. Safari, B. & Gasore, J. (2010). A statistical investigation of wind characteristics and wind energy potential based on the Weibull and Rayleigh models in Rwanda. Renew. Energy, 35 (12), 2874-2880.
20. Salameh, Z. And Nandu, C. V. (2010). Overview of building integrated wind energy conversion systems. IEEE Power and Energy Society General Meeting, Minneapolis, USA.
21. Saporu, F. W. O and Esbond, G. I (2015) Wind Energy Potential of Maiduguri, Borno State, Nigeria. International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064.
22. Seguro, J. & Lambert, T. (2000). Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis. J. Wind Eng. Ind. Aerodyn. 85 (1), 75-84.
23. Sgouropoulos, N., Yao, Q and Yastremiz, C. (2014). Matching a Distribution by Matching Quantiles Estimation. Journal of the American Statistical Association. 110. 00-00. 10.1080/01621459.2014.92952.
24. Smirnov, N. (1948). Table for estimating the goodness of fit of empirical distributions.
25. Annals of Mathematical Statistics 19 (2): 279–281. doi: 10.1214/aoms/1177730256.
26. Stephens, M. A. (1986) Tests based on EDF statistics. In: D’Agostino, R. B. and Stephens, M. A., eds.: Goodness-of-Fit Techniques. Marcel Dekker, New York.
27. Stephens, M. A. (1974): EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69, 730–737.
28. Toure, S. (2005) Investigations on the Eigen-coordinates method for the 2-parameter.
29. Weibull distribution of wind speed. Renewable Energy, vol. 30, pp. 511-521.
30. Yilmaz, V and Çelik, H. E. (2004) The estimation of earthquake risk in Eskişehir, Turkey. Anadolu University Journal of Science and Technology, vol. 5, no. 2, pp. 279-283.
31. Zhou, J., Erdem, E., Li, G., & Shi, J. (2010). Comprehensive evaluation of wind speed distribution models: A case study for North Dakota sites. Energy Convers. Manag., 51 (7), 1449-1458.