Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation

Jones Asante Manu; Nathaniel Howard; Bismark Kwao Nkansah

doi:doi:10.11648/j.ijsd.20241002.13

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Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation

Jones Asante Manu^*, Nathaniel Howard, Bismark Kwao Nkansah

Published in International Journal of Statistical Distributions and Applications (Volume 10, Issue 2)

Received: 30 April 2024 Accepted: 24 May 2024 Published: 26 June 2024

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Abstract

The scope for generating high-rank transmuted distributions has expanded beyond the cubic to achieve improved performance in baseline distributions such as those of the Gamma type. This paper develops a Quartic Rank Transmutation Distribution (QRTD), a new family of transmuted distributions with enhanced flexibility for modelling complex data problems, including those with multi-modal distributions. Application is carried out to obtain a transmuted exponential distribution (QTED). Various characteristics of the new exponential distribution are presented, including the cumulative distribution function, the reliability and hazard functions, moments, and relevant order statistics. These features support the legitimacy and robustness of the proposed QTED. Additionally, the paper identifies specific parameter ranges that exhibit notable behaviours in the new distribution and its survival quantities. The maximum likelihood estimates of parameters are described, with simulation studies indicating that their precision improves with larger sample sizes. The performance of the QTED is found to be superior to existing lower-rank cubic and quadratic transmuted exponential distributions based on information criteria using real lifetime data. The applications demonstrate that the high-rank transmutation map could be instrumental in obtaining new transmutations of other relevant distributions with improved performance. This development signifies a major advancement in the field of probability distributions, offering more sophisticated tools for statisticians and researchers to model and analyse complex data patterns more accurately and effectively. Thus, the QRTD and its applications hold significant promise for future research and practical implementations in various statistical and applied fields.

Published in	International Journal of Statistical Distributions and Applications (Volume 10, Issue 2)
DOI	10.11648/j.ijsd.20241002.13
Page(s)	38-47
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

Quartic Transmutation, Transmuted Exponential Distribution, Parameter Estimation, Order Statistics

References

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[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]	Cordeiro, G. M. & Castro, M. de. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81: 883-898.
[7]	Eugene, N., Lee, C. & Famoye, F., (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods, 31: 497-512.
[8]	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. https://doi.org/10.1080/00949655.2017.1344239
[9]	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
[10]	Merovci, F. & Puka, L. (2014). Transmuted Pareto Distribution. ProbStat Forum 7: 1-11.
[11]	Owoloko, E. A., Oguntunde, P.E. & Adejumo, A. O. (2015). Performance rating of the transmuted exponential distribution: An analytical approach. Springer Plus, 4: 8- 18, https://doi.org/10.1186/s40064-015-1590-6
[12]	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
[13]	Rahman, M. M., Al-Zahrani, B., & Shahbaz, M. Q. (2018a). Cubic Transmuted Pareto Distribution. Annals of Data Science, 1-18.
[14]	Rahman, M. M., Al-Zahrani, B., & Shahbaz, M. Q. (2018). A General Transmuted Family of Distributions. Pak J Stat Oper Res, 14: 451-469, https://doi.org/10.18187/pjsor.v14i2.2334
[15]	Shaw, W. T. & Buckley, I. R. C. (2009). The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. Research report.
[16]	Tahir, M. H. & Cordeiro, G. M. (2016). Compounding of distributions: a survey and new generalized classes. Journal of Statistical Distributions and Applications, 3, 1-35.

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APA Style

Manu, J. A., Howard, N., Nkansah, B. K. (2024). Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation. International Journal of Statistical Distributions and Applications, 10(2), 38-47. https://doi.org/10.11648/j.ijsd.20241002.13

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ACS Style

Manu, J. A.; Howard, N.; Nkansah, B. K. Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation. Int. J. Stat. Distrib. Appl. 2024, 10(2), 38-47. doi: 10.11648/j.ijsd.20241002.13

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AMA Style

Manu JA, Howard N, Nkansah BK. Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation. Int J Stat Distrib Appl. 2024;10(2):38-47. doi: 10.11648/j.ijsd.20241002.13

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@article{10.11648/j.ijsd.20241002.13,
  author = {Jones Asante Manu and Nathaniel Howard and Bismark Kwao Nkansah},
  title = {Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {10},
  number = {2},
  pages = {38-47},
  doi = {10.11648/j.ijsd.20241002.13},
  url = {https://doi.org/10.11648/j.ijsd.20241002.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20241002.13},
  abstract = {The scope for generating high-rank transmuted distributions has expanded beyond the cubic to achieve improved performance in baseline distributions such as those of the Gamma type. This paper develops a Quartic Rank Transmutation Distribution (QRTD), a new family of transmuted distributions with enhanced flexibility for modelling complex data problems, including those with multi-modal distributions. Application is carried out to obtain a transmuted exponential distribution (QTED). Various characteristics of the new exponential distribution are presented, including the cumulative distribution function, the reliability and hazard functions, moments, and relevant order statistics. These features support the legitimacy and robustness of the proposed QTED. Additionally, the paper identifies specific parameter ranges that exhibit notable behaviours in the new distribution and its survival quantities. The maximum likelihood estimates of parameters are described, with simulation studies indicating that their precision improves with larger sample sizes. The performance of the QTED is found to be superior to existing lower-rank cubic and quadratic transmuted exponential distributions based on information criteria using real lifetime data. The applications demonstrate that the high-rank transmutation map could be instrumental in obtaining new transmutations of other relevant distributions with improved performance. This development signifies a major advancement in the field of probability distributions, offering more sophisticated tools for statisticians and researchers to model and analyse complex data patterns more accurately and effectively. Thus, the QRTD and its applications hold significant promise for future research and practical implementations in various statistical and applied fields.},
 year = {2024}
}

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TY  - JOUR
T1  - Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation
AU  - Jones Asante Manu
AU  - Nathaniel Howard
AU  - Bismark Kwao Nkansah
Y1  - 2024/06/26
PY  - 2024
N1  - https://doi.org/10.11648/j.ijsd.20241002.13
DO  - 10.11648/j.ijsd.20241002.13
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  - 38
EP  - 47
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20241002.13
AB  - The scope for generating high-rank transmuted distributions has expanded beyond the cubic to achieve improved performance in baseline distributions such as those of the Gamma type. This paper develops a Quartic Rank Transmutation Distribution (QRTD), a new family of transmuted distributions with enhanced flexibility for modelling complex data problems, including those with multi-modal distributions. Application is carried out to obtain a transmuted exponential distribution (QTED). Various characteristics of the new exponential distribution are presented, including the cumulative distribution function, the reliability and hazard functions, moments, and relevant order statistics. These features support the legitimacy and robustness of the proposed QTED. Additionally, the paper identifies specific parameter ranges that exhibit notable behaviours in the new distribution and its survival quantities. The maximum likelihood estimates of parameters are described, with simulation studies indicating that their precision improves with larger sample sizes. The performance of the QTED is found to be superior to existing lower-rank cubic and quadratic transmuted exponential distributions based on information criteria using real lifetime data. The applications demonstrate that the high-rank transmutation map could be instrumental in obtaining new transmutations of other relevant distributions with improved performance. This development signifies a major advancement in the field of probability distributions, offering more sophisticated tools for statisticians and researchers to model and analyse complex data patterns more accurately and effectively. Thus, the QRTD and its applications hold significant promise for future research and practical implementations in various statistical and applied fields.
VL  - 10
IS  - 2
ER  -

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Author Information

Jones Asante Manu

Department of Business Studies, Lancaster University Ghana, Accra, Ghana

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Nathaniel Howard

Department of Statistics, University of Cape Coast, Cape Coast, Ghana

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Bismark Kwao Nkansah

Department of Statistics, University of Cape Coast, Cape Coast, Ghana

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Plain Text BibTeX RIS

APA Style

Manu, J. A., Howard, N., Nkansah, B. K. (2024). Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation. International Journal of Statistical Distributions and Applications, 10(2), 38-47. https://doi.org/10.11648/j.ijsd.20241002.13

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ACS Style

Manu, J. A.; Howard, N.; Nkansah, B. K. Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation. Int. J. Stat. Distrib. Appl. 2024, 10(2), 38-47. doi: 10.11648/j.ijsd.20241002.13

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AMA Style

Manu JA, Howard N, Nkansah BK. Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation. Int J Stat Distrib Appl. 2024;10(2):38-47. doi: 10.11648/j.ijsd.20241002.13

Copy | Download

@article{10.11648/j.ijsd.20241002.13,
  author = {Jones Asante Manu and Nathaniel Howard and Bismark Kwao Nkansah},
  title = {Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {10},
  number = {2},
  pages = {38-47},
  doi = {10.11648/j.ijsd.20241002.13},
  url = {https://doi.org/10.11648/j.ijsd.20241002.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20241002.13},
  abstract = {The scope for generating high-rank transmuted distributions has expanded beyond the cubic to achieve improved performance in baseline distributions such as those of the Gamma type. This paper develops a Quartic Rank Transmutation Distribution (QRTD), a new family of transmuted distributions with enhanced flexibility for modelling complex data problems, including those with multi-modal distributions. Application is carried out to obtain a transmuted exponential distribution (QTED). Various characteristics of the new exponential distribution are presented, including the cumulative distribution function, the reliability and hazard functions, moments, and relevant order statistics. These features support the legitimacy and robustness of the proposed QTED. Additionally, the paper identifies specific parameter ranges that exhibit notable behaviours in the new distribution and its survival quantities. The maximum likelihood estimates of parameters are described, with simulation studies indicating that their precision improves with larger sample sizes. The performance of the QTED is found to be superior to existing lower-rank cubic and quadratic transmuted exponential distributions based on information criteria using real lifetime data. The applications demonstrate that the high-rank transmutation map could be instrumental in obtaining new transmutations of other relevant distributions with improved performance. This development signifies a major advancement in the field of probability distributions, offering more sophisticated tools for statisticians and researchers to model and analyse complex data patterns more accurately and effectively. Thus, the QRTD and its applications hold significant promise for future research and practical implementations in various statistical and applied fields.},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Quartic Transmuted Exponential Distribution: Characteristics and Parameter Estimation
AU  - Jones Asante Manu
AU  - Nathaniel Howard
AU  - Bismark Kwao Nkansah
Y1  - 2024/06/26
PY  - 2024
N1  - https://doi.org/10.11648/j.ijsd.20241002.13
DO  - 10.11648/j.ijsd.20241002.13
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  - 38
EP  - 47
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20241002.13
AB  - The scope for generating high-rank transmuted distributions has expanded beyond the cubic to achieve improved performance in baseline distributions such as those of the Gamma type. This paper develops a Quartic Rank Transmutation Distribution (QRTD), a new family of transmuted distributions with enhanced flexibility for modelling complex data problems, including those with multi-modal distributions. Application is carried out to obtain a transmuted exponential distribution (QTED). Various characteristics of the new exponential distribution are presented, including the cumulative distribution function, the reliability and hazard functions, moments, and relevant order statistics. These features support the legitimacy and robustness of the proposed QTED. Additionally, the paper identifies specific parameter ranges that exhibit notable behaviours in the new distribution and its survival quantities. The maximum likelihood estimates of parameters are described, with simulation studies indicating that their precision improves with larger sample sizes. The performance of the QTED is found to be superior to existing lower-rank cubic and quadratic transmuted exponential distributions based on information criteria using real lifetime data. The applications demonstrate that the high-rank transmutation map could be instrumental in obtaining new transmutations of other relevant distributions with improved performance. This development signifies a major advancement in the field of probability distributions, offering more sophisticated tools for statisticians and researchers to model and analyse complex data patterns more accurately and effectively. Thus, the QRTD and its applications hold significant promise for future research and practical implementations in various statistical and applied fields.
VL  - 10
IS  - 2
ER  -

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