Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application

Jones Asante Manu; Samuel Darkwah

doi:doi:10.11648/j.ijsd.20241003.12

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Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application

Jones Asante Manu^*

, Samuel Darkwah

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

Received: 8 July 2024 Accepted: 20 September 2024 Published: 31 October 2024

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Abstract

This study introduces and evaluates the Cubic Transmuted Ailamujia Distribution (CTAD), a novel distribution developed using CRT-type I as a generator and the Ailamujia distribution as a baseline. We derived several statistical quantities, including density and distribution functions, hazard and survival functions, moments, and order statistics. The performance of the CTAD was compared against several established models using three distinct datasets: exceedances of flood peaks from the Wheaton River (Dataset I), cumulative COVID-19 death counts for Ghana (Dataset II), and daily confirmed COVID-19 cases for Ghana (Dataset III). The CTAD showed competitive performance, often outperforming traditional models such as the QTAD and Ailamujia distributions in Dataset I, and demonstrating strong performance relative to the CTGD, CTFD, and CTWD distributions in Dataset II. In Dataset III, while the CTAD was competitive, it was outperformed by the EWD and GGD in terms of AIC and BIC. Overall, the CTAD proves to be a robust and flexible distribution for modelling complex data patterns, though alternative distributions may offer better fits in specific scenarios. These findings underscore the CTAD’s potential as a valuable tool in statistical modelling and suggest opportunities for further research and refinement.

Published in	International Journal of Statistical Distributions and Applications (Volume 10, Issue 3)
DOI	10.11648/j.ijsd.20241003.12
Page(s)	60-77
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

Ailamujia Distribution, Cubic Rank Transmutation, Maximum Likelihood Estimation, Order Statistics, Moments, Simulation

References

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[2]	Aijaz, A., Ahmad, A., & Tripathi, R. (2020). Inverse analogue of Ailamujia distribution with statistical properties and applications. Asian Research Journal of Mathematics, 16(9), 36-46.
[3]	AL-Kadim, K. A., & Mohammed, M. H. (2017). The Cubic Transmuted Weibull Distribution. Journal of Babylon University/Pure and Applied Sciences, 25(3), 862-876.
[4]	Burr, I. W. (1942). Cumulative frequency functions. Annals of Mathematical Statistics, 13, 215-232. https://doi.org/10.1214/aoms/1177731607
[5]	Celik, N. (2018). Some Cubic Rank Transmuted Distributions. Journal of Applied Mathematics, Statistics and Informatics, 14(2), 27-43.
[6]	Choulakian, V., & Stephens, M. A. (2001). Goodness- of-fit tests for the generalized Pareto distribution. Technometrics, 43(4), 478-484.
[7]	Cordeiro, G. M., & Castro, M. de. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81, 883-898.
[8]	Eugene, N., Lee, C., & Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods, 31, 497-512.
[9]	Granzotto, D. C. T., Louzada, F., & Balakrishnan, N. (2017). Cubic Rank Transmuted Distributions: Inferential Issues and Applications. Journal of Statistical Computation and Simulation, 87(14), 2760-2778.
[10]	Marshall, A. W., & Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84, 641-652. https://doi.org/10.1093/biomet/84.3.641
[11]	Lv, H. Q., Gao, L. H., & Chen, C. L. (2002). Ailamujia distribution and its application in supportability data analysis. Journal of Academy of Armored Force Engineering, 16(3), 48-52.
[12]	Our World in Data. (2024). Coronavirus pandemic (COVID-19). https://ourworldindata.org/coronavirus
[13]	Pan, G. T., Wang, C. L., Huang, Y. B., & Dang, M. T. (2009). The research of interval estimation and hypothetical test of small sample of Ailamujia distribution. Application of Statistics and Management, 28(3), 468-472.
[14]	Pearson, K. (1895). Contributions to the mathematical theory of evolution, II: Skew variation in homogeneous material. Philosophical Transactions of the Royal Society, 186, 343-414. https://doi.org/10.1098/rsta.1895.0010
[15]	Rather, A., Subramanian, C., Shafi, S., Malik, K. A., Ahmad, P. J., Para, B. A., & Jan, T. A. (2018). New size biased distribution with Applications in Engineering and Medical Science. IJSRMSS, 5(4), 75-85.
[16]	Rahman, M. M., AL-Zahrani, B., & Shahbaz, M. Q. (2018). A General Transmuted Family of Distributions. Pakistan Journal of Statistics and Operation Research, 14(2), 451-469.
[17]	Uzma, J., Kawsar, F., & Ahmad, S. P. (2017). On weighted Ailamujia distribution and its applications to life time data. Journal of Statistics Applications and Probability an International Journal, 6(3), 619-633.

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APA Style

Manu, J. A., Darkwah, S. (2024). Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application. International Journal of Statistical Distributions and Applications, 10(3), 60-77. https://doi.org/10.11648/j.ijsd.20241003.12

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ACS Style

Manu, J. A.; Darkwah, S. Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application. Int. J. Stat. Distrib. Appl. 2024, 10(3), 60-77. doi: 10.11648/j.ijsd.20241003.12

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AMA Style

Manu JA, Darkwah S. Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application. Int J Stat Distrib Appl. 2024;10(3):60-77. doi: 10.11648/j.ijsd.20241003.12

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@article{10.11648/j.ijsd.20241003.12,
  author = {Jones Asante Manu and Samuel Darkwah},
  title = {Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {10},
  number = {3},
  pages = {60-77},
  doi = {10.11648/j.ijsd.20241003.12},
  url = {https://doi.org/10.11648/j.ijsd.20241003.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20241003.12},
  abstract = {This study introduces and evaluates the Cubic Transmuted Ailamujia Distribution (CTAD), a novel distribution developed using CRT-type I as a generator and the Ailamujia distribution as a baseline. We derived several statistical quantities, including density and distribution functions, hazard and survival functions, moments, and order statistics. The performance of the CTAD was compared against several established models using three distinct datasets: exceedances of flood peaks from the Wheaton River (Dataset I), cumulative COVID-19 death counts for Ghana (Dataset II), and daily confirmed COVID-19 cases for Ghana (Dataset III). The CTAD showed competitive performance, often outperforming traditional models such as the QTAD and Ailamujia distributions in Dataset I, and demonstrating strong performance relative to the CTGD, CTFD, and CTWD distributions in Dataset II. In Dataset III, while the CTAD was competitive, it was outperformed by the EWD and GGD in terms of AIC and BIC. Overall, the CTAD proves to be a robust and flexible distribution for modelling complex data patterns, though alternative distributions may offer better fits in specific scenarios. These findings underscore the CTAD’s potential as a valuable tool in statistical modelling and suggest opportunities for further research and refinement.},
 year = {2024}
}

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TY  - JOUR
T1  - Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application
AU  - Jones Asante Manu
AU  - Samuel Darkwah
Y1  - 2024/10/31
PY  - 2024
N1  - https://doi.org/10.11648/j.ijsd.20241003.12
DO  - 10.11648/j.ijsd.20241003.12
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  - 60
EP  - 77
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20241003.12
AB  - This study introduces and evaluates the Cubic Transmuted Ailamujia Distribution (CTAD), a novel distribution developed using CRT-type I as a generator and the Ailamujia distribution as a baseline. We derived several statistical quantities, including density and distribution functions, hazard and survival functions, moments, and order statistics. The performance of the CTAD was compared against several established models using three distinct datasets: exceedances of flood peaks from the Wheaton River (Dataset I), cumulative COVID-19 death counts for Ghana (Dataset II), and daily confirmed COVID-19 cases for Ghana (Dataset III). The CTAD showed competitive performance, often outperforming traditional models such as the QTAD and Ailamujia distributions in Dataset I, and demonstrating strong performance relative to the CTGD, CTFD, and CTWD distributions in Dataset II. In Dataset III, while the CTAD was competitive, it was outperformed by the EWD and GGD in terms of AIC and BIC. Overall, the CTAD proves to be a robust and flexible distribution for modelling complex data patterns, though alternative distributions may offer better fits in specific scenarios. These findings underscore the CTAD’s potential as a valuable tool in statistical modelling and suggest opportunities for further research and refinement.
VL  - 10
IS  - 3
ER  -

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Author Information

Jones Asante Manu

Business Studies Department, Lancaster University Ghana, Accra, Ghana

Contact Email

http://orcid.org/0009-0008-5147-6128
Samuel Darkwah

Mathematics Department, Methodist University Ghana, Accra, Ghana

Contact Email

http://orcid.org/0009-0002-9215-6143

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Plain Text BibTeX RIS

APA Style

Manu, J. A., Darkwah, S. (2024). Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application. International Journal of Statistical Distributions and Applications, 10(3), 60-77. https://doi.org/10.11648/j.ijsd.20241003.12

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ACS Style

Manu, J. A.; Darkwah, S. Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application. Int. J. Stat. Distrib. Appl. 2024, 10(3), 60-77. doi: 10.11648/j.ijsd.20241003.12

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AMA Style

Manu JA, Darkwah S. Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application. Int J Stat Distrib Appl. 2024;10(3):60-77. doi: 10.11648/j.ijsd.20241003.12

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@article{10.11648/j.ijsd.20241003.12,
  author = {Jones Asante Manu and Samuel Darkwah},
  title = {Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {10},
  number = {3},
  pages = {60-77},
  doi = {10.11648/j.ijsd.20241003.12},
  url = {https://doi.org/10.11648/j.ijsd.20241003.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20241003.12},
  abstract = {This study introduces and evaluates the Cubic Transmuted Ailamujia Distribution (CTAD), a novel distribution developed using CRT-type I as a generator and the Ailamujia distribution as a baseline. We derived several statistical quantities, including density and distribution functions, hazard and survival functions, moments, and order statistics. The performance of the CTAD was compared against several established models using three distinct datasets: exceedances of flood peaks from the Wheaton River (Dataset I), cumulative COVID-19 death counts for Ghana (Dataset II), and daily confirmed COVID-19 cases for Ghana (Dataset III). The CTAD showed competitive performance, often outperforming traditional models such as the QTAD and Ailamujia distributions in Dataset I, and demonstrating strong performance relative to the CTGD, CTFD, and CTWD distributions in Dataset II. In Dataset III, while the CTAD was competitive, it was outperformed by the EWD and GGD in terms of AIC and BIC. Overall, the CTAD proves to be a robust and flexible distribution for modelling complex data patterns, though alternative distributions may offer better fits in specific scenarios. These findings underscore the CTAD’s potential as a valuable tool in statistical modelling and suggest opportunities for further research and refinement.},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Cubic Transmuted Ailamujia Distribution - Type I: Statistical Properties and Application
AU  - Jones Asante Manu
AU  - Samuel Darkwah
Y1  - 2024/10/31
PY  - 2024
N1  - https://doi.org/10.11648/j.ijsd.20241003.12
DO  - 10.11648/j.ijsd.20241003.12
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  - 60
EP  - 77
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20241003.12
AB  - This study introduces and evaluates the Cubic Transmuted Ailamujia Distribution (CTAD), a novel distribution developed using CRT-type I as a generator and the Ailamujia distribution as a baseline. We derived several statistical quantities, including density and distribution functions, hazard and survival functions, moments, and order statistics. The performance of the CTAD was compared against several established models using three distinct datasets: exceedances of flood peaks from the Wheaton River (Dataset I), cumulative COVID-19 death counts for Ghana (Dataset II), and daily confirmed COVID-19 cases for Ghana (Dataset III). The CTAD showed competitive performance, often outperforming traditional models such as the QTAD and Ailamujia distributions in Dataset I, and demonstrating strong performance relative to the CTGD, CTFD, and CTWD distributions in Dataset II. In Dataset III, while the CTAD was competitive, it was outperformed by the EWD and GGD in terms of AIC and BIC. Overall, the CTAD proves to be a robust and flexible distribution for modelling complex data patterns, though alternative distributions may offer better fits in specific scenarios. These findings underscore the CTAD’s potential as a valuable tool in statistical modelling and suggest opportunities for further research and refinement.
VL  - 10
IS  - 3
ER  -

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