Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique

Otieno Okumu Kevin; John Matuya; Muthiga Nganga

doi:doi:10.11648/j.ajtas.20211006.11

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Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique

Otieno Okumu Kevin, John Matuya, Muthiga Nganga

Published in American Journal of Theoretical and Applied Statistics (Volume 10, Issue 6)

Received: 10 March 2021 Accepted: 22 March 2021 Published: 10 November 2021

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Abstract

From the past studies, we realized that minimum distance estimation technique is not commonly used for fitting wind speed data to a distribution yet it is believed to the best alternative for Maximum Likelihood Estimation (MLE) method which is known to give good estimates than Least Square Estimates (LSE) and Method of Moments (MOM). To achieve this, the study aims at fitting data to a probability distribution using minimum distance estimation techniques to find the best distribution. The study uses wind speed data from five sites in Narok county namely; Irbaan primary, Imortott primary, Mara conservancy, Oldrkesi and Maasai Mara University. The best wind speed models were examined using the Cullen and Frey graph and a suitability test on the models done using Kolmogorov-Smirnov statistical test of goodness of fit. The wind speed data are fitted to the recommended distributions using minimum distance estimation techniques. The best distribution was identified using Akaike's Information Criterion (AIC) and Bayesian Information criterion (BIC). From the distribution comparison for the two and three parameter distributions, gamma is the best in all cases. Gamma with three parameter distribution gives lower AIC and BIC values and model comparison test showing that gamma 3-parameter is the better than gamma with 2-parameters. The study concluded that gamma distribution with three parameters is the best distribution for fitting wind speed data with the three parameters given as; threshold parameter of 0.1174, shape parameter of 1.8646 and scale parameter of 0.9937.

Published in	American Journal of Theoretical and Applied Statistics (Volume 10, Issue 6)
DOI	10.11648/j.ajtas.20211006.11
Page(s)	226-232
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

Minimum Distance Estimation (MDE), Akaike’s Information Criterion (AIC), Bayesian Information Criterion (BIC), Distribution

References

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APA Style

Otieno Okumu Kevin, John Matuya, Muthiga Nganga. (2021). Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique. American Journal of Theoretical and Applied Statistics, 10(6), 226-232. https://doi.org/10.11648/j.ajtas.20211006.11

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ACS Style

Otieno Okumu Kevin; John Matuya; Muthiga Nganga. Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique. Am. J. Theor. Appl. Stat. 2021, 10(6), 226-232. doi: 10.11648/j.ajtas.20211006.11

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AMA Style

Otieno Okumu Kevin, John Matuya, Muthiga Nganga. Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique. Am J Theor Appl Stat. 2021;10(6):226-232. doi: 10.11648/j.ajtas.20211006.11

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@article{10.11648/j.ajtas.20211006.11,
  author = {Otieno Okumu Kevin and John Matuya and Muthiga Nganga},
  title = {Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {10},
  number = {6},
  pages = {226-232},
  doi = {10.11648/j.ajtas.20211006.11},
  url = {https://doi.org/10.11648/j.ajtas.20211006.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211006.11},
  abstract = {From the past studies, we realized that minimum distance estimation technique is not commonly used for fitting wind speed data to a distribution yet it is believed to the best alternative for Maximum Likelihood Estimation (MLE) method which is known to give good estimates than Least Square Estimates (LSE) and Method of Moments (MOM). To achieve this, the study aims at fitting data to a probability distribution using minimum distance estimation techniques to find the best distribution. The study uses wind speed data from five sites in Narok county namely; Irbaan primary, Imortott primary, Mara conservancy, Oldrkesi and Maasai Mara University. The best wind speed models were examined using the Cullen and Frey graph and a suitability test on the models done using Kolmogorov-Smirnov statistical test of goodness of fit. The wind speed data are fitted to the recommended distributions using minimum distance estimation techniques. The best distribution was identified using Akaike's Information Criterion (AIC) and Bayesian Information criterion (BIC). From the distribution comparison for the two and three parameter distributions, gamma is the best in all cases. Gamma with three parameter distribution gives lower AIC and BIC values and model comparison test showing that gamma 3-parameter is the better than gamma with 2-parameters. The study concluded that gamma distribution with three parameters is the best distribution for fitting wind speed data with the three parameters given as; threshold parameter of 0.1174, shape parameter of 1.8646 and scale parameter of 0.9937.},
 year = {2021}
}

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TY  - JOUR
T1  - Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique
AU  - Otieno Okumu Kevin
AU  - John Matuya
AU  - Muthiga Nganga
Y1  - 2021/11/10
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtas.20211006.11
DO  - 10.11648/j.ajtas.20211006.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 226
EP  - 232
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20211006.11
AB  - From the past studies, we realized that minimum distance estimation technique is not commonly used for fitting wind speed data to a distribution yet it is believed to the best alternative for Maximum Likelihood Estimation (MLE) method which is known to give good estimates than Least Square Estimates (LSE) and Method of Moments (MOM). To achieve this, the study aims at fitting data to a probability distribution using minimum distance estimation techniques to find the best distribution. The study uses wind speed data from five sites in Narok county namely; Irbaan primary, Imortott primary, Mara conservancy, Oldrkesi and Maasai Mara University. The best wind speed models were examined using the Cullen and Frey graph and a suitability test on the models done using Kolmogorov-Smirnov statistical test of goodness of fit. The wind speed data are fitted to the recommended distributions using minimum distance estimation techniques. The best distribution was identified using Akaike's Information Criterion (AIC) and Bayesian Information criterion (BIC). From the distribution comparison for the two and three parameter distributions, gamma is the best in all cases. Gamma with three parameter distribution gives lower AIC and BIC values and model comparison test showing that gamma 3-parameter is the better than gamma with 2-parameters. The study concluded that gamma distribution with three parameters is the best distribution for fitting wind speed data with the three parameters given as; threshold parameter of 0.1174, shape parameter of 1.8646 and scale parameter of 0.9937.
VL  - 10
IS  - 6
ER  -

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Author Information

Otieno Okumu Kevin

Department of Mathematics and physical sciences, Maasai Mara University, Narok, Kenya
John Matuya

Department of Mathematics and physical sciences, Maasai Mara University, Narok, Kenya
Muthiga Nganga

Department of Mathematics and physical sciences, Maasai Mara University, Narok, Kenya

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APA Style

Otieno Okumu Kevin, John Matuya, Muthiga Nganga. (2021). Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique. American Journal of Theoretical and Applied Statistics, 10(6), 226-232. https://doi.org/10.11648/j.ajtas.20211006.11

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ACS Style

Otieno Okumu Kevin; John Matuya; Muthiga Nganga. Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique. Am. J. Theor. Appl. Stat. 2021, 10(6), 226-232. doi: 10.11648/j.ajtas.20211006.11

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AMA Style

Otieno Okumu Kevin, John Matuya, Muthiga Nganga. Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique. Am J Theor Appl Stat. 2021;10(6):226-232. doi: 10.11648/j.ajtas.20211006.11

Copy | Download

@article{10.11648/j.ajtas.20211006.11,
  author = {Otieno Okumu Kevin and John Matuya and Muthiga Nganga},
  title = {Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {10},
  number = {6},
  pages = {226-232},
  doi = {10.11648/j.ajtas.20211006.11},
  url = {https://doi.org/10.11648/j.ajtas.20211006.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211006.11},
  abstract = {From the past studies, we realized that minimum distance estimation technique is not commonly used for fitting wind speed data to a distribution yet it is believed to the best alternative for Maximum Likelihood Estimation (MLE) method which is known to give good estimates than Least Square Estimates (LSE) and Method of Moments (MOM). To achieve this, the study aims at fitting data to a probability distribution using minimum distance estimation techniques to find the best distribution. The study uses wind speed data from five sites in Narok county namely; Irbaan primary, Imortott primary, Mara conservancy, Oldrkesi and Maasai Mara University. The best wind speed models were examined using the Cullen and Frey graph and a suitability test on the models done using Kolmogorov-Smirnov statistical test of goodness of fit. The wind speed data are fitted to the recommended distributions using minimum distance estimation techniques. The best distribution was identified using Akaike's Information Criterion (AIC) and Bayesian Information criterion (BIC). From the distribution comparison for the two and three parameter distributions, gamma is the best in all cases. Gamma with three parameter distribution gives lower AIC and BIC values and model comparison test showing that gamma 3-parameter is the better than gamma with 2-parameters. The study concluded that gamma distribution with three parameters is the best distribution for fitting wind speed data with the three parameters given as; threshold parameter of 0.1174, shape parameter of 1.8646 and scale parameter of 0.9937.},
 year = {2021}
}

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TY  - JOUR
T1  - Fitting Wind Speed to a Probability Distribution Using Minimum Distance Estimation Technique
AU  - Otieno Okumu Kevin
AU  - John Matuya
AU  - Muthiga Nganga
Y1  - 2021/11/10
PY  - 2021
N1  - https://doi.org/10.11648/j.ajtas.20211006.11
DO  - 10.11648/j.ajtas.20211006.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 226
EP  - 232
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20211006.11
AB  - From the past studies, we realized that minimum distance estimation technique is not commonly used for fitting wind speed data to a distribution yet it is believed to the best alternative for Maximum Likelihood Estimation (MLE) method which is known to give good estimates than Least Square Estimates (LSE) and Method of Moments (MOM). To achieve this, the study aims at fitting data to a probability distribution using minimum distance estimation techniques to find the best distribution. The study uses wind speed data from five sites in Narok county namely; Irbaan primary, Imortott primary, Mara conservancy, Oldrkesi and Maasai Mara University. The best wind speed models were examined using the Cullen and Frey graph and a suitability test on the models done using Kolmogorov-Smirnov statistical test of goodness of fit. The wind speed data are fitted to the recommended distributions using minimum distance estimation techniques. The best distribution was identified using Akaike's Information Criterion (AIC) and Bayesian Information criterion (BIC). From the distribution comparison for the two and three parameter distributions, gamma is the best in all cases. Gamma with three parameter distribution gives lower AIC and BIC values and model comparison test showing that gamma 3-parameter is the better than gamma with 2-parameters. The study concluded that gamma distribution with three parameters is the best distribution for fitting wind speed data with the three parameters given as; threshold parameter of 0.1174, shape parameter of 1.8646 and scale parameter of 0.9937.
VL  - 10
IS  - 6
ER  -

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