Transmuted Power Gumbel Distribution: Estimation and Applications

Ahmed Ali Hurairah; Nasr Tawfiq Almazaqi

doi:doi:10.11648/j.ijsd.20241003.11

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Transmuted Power Gumbel Distribution: Estimation and Applications

Ahmed Ali Hurairah^*, Nasr Tawfiq Almazaqi

Published in International Journal of Statistical Distributions and Applications (Volume 10, Issue 3)

Received: 6 August 2024 Accepted: 5 September 2024 Published: 23 September 2024

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Abstract

In recent years, generalized distributions have been widely studied in statistics as they possess flexibility in applications. This is justified because the traditional distributions often do not provide good fit in relation to the real data set studied. This paper develops a Power Gumbel distribution using the quadratic rank transmutation map (QRTM). The new generalization is called the transmuted Power-Gumbel distribution. Various mathematical properties of this distribution including moments, moment generating function, quantile function, mean deviation and order statistics were also studied. These features support the legitimacy and robustness of the proposed distribution. The maximum likelihood method is used for estimating the model parameters, and the finite sample performance of the estimators are assessed by simulation studies indicating that their precision improves with larger sample sizes. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. Finally, the usefulness of the proposed model is illustrated in an application to two real data sets and conclude that the four-parameter transmuted Power Gumbel distribution provides better fit than the other five models.

Published in	International Journal of Statistical Distributions and Applications (Volume 10, Issue 3)
DOI	10.11648/j.ijsd.20241003.11
Page(s)	48-59
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

Gumbel Distribution, Transmuted Power Gumbel Distribution, Parameter Estimation, Asymptotic Confidence Intervals, Quadratic Rank Transmutation

References

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APA Style

Hurairah, A. A., Almazaqi, N. T. (2024). Transmuted Power Gumbel Distribution: Estimation and Applications. International Journal of Statistical Distributions and Applications, 10(3), 48-59. https://doi.org/10.11648/j.ijsd.20241003.11

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ACS Style

Hurairah, A. A.; Almazaqi, N. T. Transmuted Power Gumbel Distribution: Estimation and Applications. Int. J. Stat. Distrib. Appl. 2024, 10(3), 48-59. doi: 10.11648/j.ijsd.20241003.11

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AMA Style

Hurairah AA, Almazaqi NT. Transmuted Power Gumbel Distribution: Estimation and Applications. Int J Stat Distrib Appl. 2024;10(3):48-59. doi: 10.11648/j.ijsd.20241003.11

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@article{10.11648/j.ijsd.20241003.11,
  author = {Ahmed Ali Hurairah and Nasr Tawfiq Almazaqi},
  title = {Transmuted Power Gumbel Distribution: Estimation and Applications
},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {10},
  number = {3},
  pages = {48-59},
  doi = {10.11648/j.ijsd.20241003.11},
  url = {https://doi.org/10.11648/j.ijsd.20241003.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20241003.11},
  abstract = {In recent years, generalized distributions have been widely studied in statistics as they possess flexibility in applications. This is justified because the traditional distributions often do not provide good fit in relation to the real data set studied. This paper develops a Power Gumbel distribution using the quadratic rank transmutation map (QRTM). The new generalization is called the transmuted Power-Gumbel distribution. Various mathematical properties of this distribution including moments, moment generating function, quantile function, mean deviation and order statistics were also studied. These features support the legitimacy and robustness of the proposed distribution. The maximum likelihood method is used for estimating the model parameters, and the finite sample performance of the estimators are assessed by simulation studies indicating that their precision improves with larger sample sizes. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. Finally, the usefulness of the proposed model is illustrated in an application to two real data sets and conclude that the four-parameter transmuted Power Gumbel distribution provides better fit than the other five models.
},
 year = {2024}
}

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TY  - JOUR
T1  - Transmuted Power Gumbel Distribution: Estimation and Applications

AU  - Ahmed Ali Hurairah
AU  - Nasr Tawfiq Almazaqi
Y1  - 2024/09/23
PY  - 2024
N1  - https://doi.org/10.11648/j.ijsd.20241003.11
DO  - 10.11648/j.ijsd.20241003.11
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  - 48
EP  - 59
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20241003.11
AB  - In recent years, generalized distributions have been widely studied in statistics as they possess flexibility in applications. This is justified because the traditional distributions often do not provide good fit in relation to the real data set studied. This paper develops a Power Gumbel distribution using the quadratic rank transmutation map (QRTM). The new generalization is called the transmuted Power-Gumbel distribution. Various mathematical properties of this distribution including moments, moment generating function, quantile function, mean deviation and order statistics were also studied. These features support the legitimacy and robustness of the proposed distribution. The maximum likelihood method is used for estimating the model parameters, and the finite sample performance of the estimators are assessed by simulation studies indicating that their precision improves with larger sample sizes. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. Finally, the usefulness of the proposed model is illustrated in an application to two real data sets and conclude that the four-parameter transmuted Power Gumbel distribution provides better fit than the other five models.

VL  - 10
IS  - 3
ER  -

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Author Information

Ahmed Ali Hurairah

Department of Statistics, Sana’a University, Sana’a, Yemen

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Nasr Tawfiq Almazaqi

Department of Mathematics, Sana’a University, Sana’a, Yemen

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Plain Text BibTeX RIS

APA Style

Hurairah, A. A., Almazaqi, N. T. (2024). Transmuted Power Gumbel Distribution: Estimation and Applications. International Journal of Statistical Distributions and Applications, 10(3), 48-59. https://doi.org/10.11648/j.ijsd.20241003.11

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ACS Style

Hurairah, A. A.; Almazaqi, N. T. Transmuted Power Gumbel Distribution: Estimation and Applications. Int. J. Stat. Distrib. Appl. 2024, 10(3), 48-59. doi: 10.11648/j.ijsd.20241003.11

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AMA Style

Hurairah AA, Almazaqi NT. Transmuted Power Gumbel Distribution: Estimation and Applications. Int J Stat Distrib Appl. 2024;10(3):48-59. doi: 10.11648/j.ijsd.20241003.11

Copy | Download

@article{10.11648/j.ijsd.20241003.11,
  author = {Ahmed Ali Hurairah and Nasr Tawfiq Almazaqi},
  title = {Transmuted Power Gumbel Distribution: Estimation and Applications
},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {10},
  number = {3},
  pages = {48-59},
  doi = {10.11648/j.ijsd.20241003.11},
  url = {https://doi.org/10.11648/j.ijsd.20241003.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20241003.11},
  abstract = {In recent years, generalized distributions have been widely studied in statistics as they possess flexibility in applications. This is justified because the traditional distributions often do not provide good fit in relation to the real data set studied. This paper develops a Power Gumbel distribution using the quadratic rank transmutation map (QRTM). The new generalization is called the transmuted Power-Gumbel distribution. Various mathematical properties of this distribution including moments, moment generating function, quantile function, mean deviation and order statistics were also studied. These features support the legitimacy and robustness of the proposed distribution. The maximum likelihood method is used for estimating the model parameters, and the finite sample performance of the estimators are assessed by simulation studies indicating that their precision improves with larger sample sizes. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. Finally, the usefulness of the proposed model is illustrated in an application to two real data sets and conclude that the four-parameter transmuted Power Gumbel distribution provides better fit than the other five models.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Transmuted Power Gumbel Distribution: Estimation and Applications

AU  - Ahmed Ali Hurairah
AU  - Nasr Tawfiq Almazaqi
Y1  - 2024/09/23
PY  - 2024
N1  - https://doi.org/10.11648/j.ijsd.20241003.11
DO  - 10.11648/j.ijsd.20241003.11
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  - 48
EP  - 59
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20241003.11
AB  - In recent years, generalized distributions have been widely studied in statistics as they possess flexibility in applications. This is justified because the traditional distributions often do not provide good fit in relation to the real data set studied. This paper develops a Power Gumbel distribution using the quadratic rank transmutation map (QRTM). The new generalization is called the transmuted Power-Gumbel distribution. Various mathematical properties of this distribution including moments, moment generating function, quantile function, mean deviation and order statistics were also studied. These features support the legitimacy and robustness of the proposed distribution. The maximum likelihood method is used for estimating the model parameters, and the finite sample performance of the estimators are assessed by simulation studies indicating that their precision improves with larger sample sizes. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. Finally, the usefulness of the proposed model is illustrated in an application to two real data sets and conclude that the four-parameter transmuted Power Gumbel distribution provides better fit than the other five models.

VL  - 10
IS  - 3
ER  -

Copy | Download