Cubic Transmuted Dagum Distribution: Properties and Applications

Adana’a Felix Chama

doi:doi:10.11648/j.ml.20210701.12

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Cubic Transmuted Dagum Distribution: Properties and Applications

Adana’a Felix Chama

Published in Mathematics Letters (Volume 7, Issue 1)

Received: 26 November 2020 Accepted: 10 December 2020 Published: 30 April 2021

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Abstract

In this article, a generalization of the new cubic transmuted Dagum (CTD) distribution is derived and have developed a cubic transmuted family of distribution. The proposed distribution includes a special cases of the new Transmuted Dagum distribution (TDD). The objectives are to model a new distribution called cubic transmuted Dagum distribution to take care of the flexibility and multimodal (complex) effect which the transmuted form of the distribution cannot handle. The work comprises of the probability density function of cubic transmuted Dagum distribution and its Cumulative distribution function and attempt was made to compare the new distribution with the transmuted form of the distribution. Various structural properties of the new distribution, including the moments, characteristic function, quantile, moment generating function, mean, variance, reliability analysis, order statistics are derived. The maximum likelihood estimation method has been proposed for the estimation of the parameters of the Cubic transmuted Dagum distribution. The usefulness of the derived model is illustrated using two data sets to compare the performance of the new distribution with the transmuted form of the distribution and also with the parent (Dagum) distribution, and it is proved that CTD distribution is a better distribution than the transmuted Dagum distribution and the Dagum distributions based on some goodness of fit measures. Therefore, we conclude that the new model fits real life data better than the transmuted form and the base distribution. Also cubic transmuted Dagum distribution attracts more applications in several areas such as engineering, survival data, economics and others.

Published in	Mathematics Letters (Volume 7, Issue 1)
DOI	10.11648/j.ml.20210701.12
Page(s)	7-18
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

Transmuted Distribution, Dagum Distribution, Reliability Function, Moment Generating Function, Maximum Likelihood Estimation

References

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[2]	Dagum, C. (1980). The generation and distribution of income, the Lorenz curve and the Gini ratio. In Silva, A. O, Cecilia, L. M & Cordeiro, G. M (2017). The extended Dagum Distribution: Properties and Application. Journal of Data Science, 13, 53-73.
[3]	Dagum, C. (1977). A new model of personal income distribution: Specification and estimation. Economie Appliquée, 30, 413-437. In Silva, A. O, Cecilia, L. M & Cordeiro, G. M (2017). The Extended Dagum Distribution: Properties and Application. Journal of Data Science, 13 53-73.
[4]	Elbatal I and Aryal G (2015). Transmuted Dagum distribution with Applications. Chilean journal of Statistics 6 (2), 31-45.
[5]	Granzotto, D. C. T., Louzada, F., and Balakrishnan, N. (2017). Cubic rank transmuted distributions: inferential issues and applications. Journal of Statistical Computation and Simulation, 87: 2760–2778, doi. 10.1080/00949655.2017.1344239.
[6]	Shahzad M. N and Asghar Z (2016). Transmuted Dagum Distribution: A more flexible and broad Shaped hazard function model. Hacettepe Journal of Mathematics and Statistics. Vol 45 (1), 227-244.
[7]	Fattorini, L. Lemmi, A. (1979) Proposta di un modello alternativo per lanalisi della distribuzione personale del reddito, Atti Giornate di Lavoro AIRO 28 (1), 89-117.
[8]	Bordley, R. F., McDonald, J. B. and Mantrala, A. (1996) Something new, something old: Paramet- ric models for the size distribution of income, Journal of Income Distribution 6 (1), 91-103.
[9]	Bandourian, R., McDonald, J. B. and Turley, R. S. (2003) A Comparison of Parametric Models of Income Distribution across Countries and Over Time, Estadistica 55, 135-152.
[10]	Alwan, F. M., Baharum, A. and Hassan, G. S (2013). Reliability Measurement for Mixed Model Failures of 33/11 Kilovolt Electric Power Distribution Stations, PloS one 8 (8), 1-8.
[11]	Bird, J (2005) basic Engineering mathematics, 4^th ed. Elsevier Publihing: India Pg 108.
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[13]	Kalaa M. I and Adamu D (2013). Solving Quintin equation by Radicals. International journal of Research and Advancement in physical science. 3 (3): 75-77.
[14]	Proschan, F. (1963). Theoretical Explanation of Observed Decreasing Failure Rate. Technometrics, 5, 375C383. https://doi.org/10.1080/00401706.1963.10490105.
[15]	Owoloko, A & Oguntunde, P & Adejumo, A O. (2015). Performance rating of the transmuted exponential distribution: an analytical approach. SpringerPlus. 4. 10.1186/s40064-015-1590-6.
[16]	Rahman, M. M., Al-Zahrani, B., Shahbaz, S. H., and Shahbaz, M. Q. (2019b). Cubic Transmuted Uniform Distribution: An Alternative to Beta and Kumaraswamy Distributions. European Journal of Pure and Applied Mathematics, 12: 1106–1121.

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Adana’a Felix Chama. (2021). Cubic Transmuted Dagum Distribution: Properties and Applications. Mathematics Letters, 7(1), 7-18. https://doi.org/10.11648/j.ml.20210701.12

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ACS Style

Adana’a Felix Chama. Cubic Transmuted Dagum Distribution: Properties and Applications. Math. Lett. 2021, 7(1), 7-18. doi: 10.11648/j.ml.20210701.12

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AMA Style

Adana’a Felix Chama. Cubic Transmuted Dagum Distribution: Properties and Applications. Math Lett. 2021;7(1):7-18. doi: 10.11648/j.ml.20210701.12

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@article{10.11648/j.ml.20210701.12,
  author = {Adana’a Felix Chama},
  title = {Cubic Transmuted Dagum Distribution: Properties and Applications},
  journal = {Mathematics Letters},
  volume = {7},
  number = {1},
  pages = {7-18},
  doi = {10.11648/j.ml.20210701.12},
  url = {https://doi.org/10.11648/j.ml.20210701.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20210701.12},
  abstract = {In this article, a generalization of the new cubic transmuted Dagum (CTD) distribution is derived and have developed a cubic transmuted family of distribution. The proposed distribution includes a special cases of the new Transmuted Dagum distribution (TDD). The objectives are to model a new distribution called cubic transmuted Dagum distribution to take care of the flexibility and multimodal (complex) effect which the transmuted form of the distribution cannot handle. The work comprises of the probability density function of cubic transmuted Dagum distribution   and its Cumulative distribution function and attempt was made to compare the new distribution with the transmuted form of the distribution. Various structural properties of the new distribution, including the moments, characteristic function, quantile, moment generating function, mean, variance, reliability analysis, order statistics are derived. The maximum likelihood estimation method has been proposed for the estimation of the parameters of the Cubic transmuted Dagum distribution. The usefulness of the derived model is illustrated using two data sets to compare the performance of the new distribution with the transmuted form of the distribution and also with the parent (Dagum) distribution, and it is proved that CTD distribution is a better distribution than the transmuted Dagum distribution and the Dagum distributions based on some goodness of fit measures. Therefore, we conclude that the new model fits real life data better than the transmuted form and the base distribution. Also cubic transmuted Dagum distribution attracts more applications in several areas such as engineering, survival data, economics and others.},
 year = {2021}
}

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TY  - JOUR
T1  - Cubic Transmuted Dagum Distribution: Properties and Applications
AU  - Adana’a Felix Chama
Y1  - 2021/04/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ml.20210701.12
DO  - 10.11648/j.ml.20210701.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 7
EP  - 18
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20210701.12
AB  - In this article, a generalization of the new cubic transmuted Dagum (CTD) distribution is derived and have developed a cubic transmuted family of distribution. The proposed distribution includes a special cases of the new Transmuted Dagum distribution (TDD). The objectives are to model a new distribution called cubic transmuted Dagum distribution to take care of the flexibility and multimodal (complex) effect which the transmuted form of the distribution cannot handle. The work comprises of the probability density function of cubic transmuted Dagum distribution   and its Cumulative distribution function and attempt was made to compare the new distribution with the transmuted form of the distribution. Various structural properties of the new distribution, including the moments, characteristic function, quantile, moment generating function, mean, variance, reliability analysis, order statistics are derived. The maximum likelihood estimation method has been proposed for the estimation of the parameters of the Cubic transmuted Dagum distribution. The usefulness of the derived model is illustrated using two data sets to compare the performance of the new distribution with the transmuted form of the distribution and also with the parent (Dagum) distribution, and it is proved that CTD distribution is a better distribution than the transmuted Dagum distribution and the Dagum distributions based on some goodness of fit measures. Therefore, we conclude that the new model fits real life data better than the transmuted form and the base distribution. Also cubic transmuted Dagum distribution attracts more applications in several areas such as engineering, survival data, economics and others.
VL  - 7
IS  - 1
ER  -

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Author Information

Adana’a Felix Chama

Department of Mathematical Sciences, Taraba State University, Jalingo, Nigeria

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APA Style

Adana’a Felix Chama. (2021). Cubic Transmuted Dagum Distribution: Properties and Applications. Mathematics Letters, 7(1), 7-18. https://doi.org/10.11648/j.ml.20210701.12

Copy | Download

ACS Style

Adana’a Felix Chama. Cubic Transmuted Dagum Distribution: Properties and Applications. Math. Lett. 2021, 7(1), 7-18. doi: 10.11648/j.ml.20210701.12

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AMA Style

Adana’a Felix Chama. Cubic Transmuted Dagum Distribution: Properties and Applications. Math Lett. 2021;7(1):7-18. doi: 10.11648/j.ml.20210701.12

Copy | Download

@article{10.11648/j.ml.20210701.12,
  author = {Adana’a Felix Chama},
  title = {Cubic Transmuted Dagum Distribution: Properties and Applications},
  journal = {Mathematics Letters},
  volume = {7},
  number = {1},
  pages = {7-18},
  doi = {10.11648/j.ml.20210701.12},
  url = {https://doi.org/10.11648/j.ml.20210701.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20210701.12},
  abstract = {In this article, a generalization of the new cubic transmuted Dagum (CTD) distribution is derived and have developed a cubic transmuted family of distribution. The proposed distribution includes a special cases of the new Transmuted Dagum distribution (TDD). The objectives are to model a new distribution called cubic transmuted Dagum distribution to take care of the flexibility and multimodal (complex) effect which the transmuted form of the distribution cannot handle. The work comprises of the probability density function of cubic transmuted Dagum distribution   and its Cumulative distribution function and attempt was made to compare the new distribution with the transmuted form of the distribution. Various structural properties of the new distribution, including the moments, characteristic function, quantile, moment generating function, mean, variance, reliability analysis, order statistics are derived. The maximum likelihood estimation method has been proposed for the estimation of the parameters of the Cubic transmuted Dagum distribution. The usefulness of the derived model is illustrated using two data sets to compare the performance of the new distribution with the transmuted form of the distribution and also with the parent (Dagum) distribution, and it is proved that CTD distribution is a better distribution than the transmuted Dagum distribution and the Dagum distributions based on some goodness of fit measures. Therefore, we conclude that the new model fits real life data better than the transmuted form and the base distribution. Also cubic transmuted Dagum distribution attracts more applications in several areas such as engineering, survival data, economics and others.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Cubic Transmuted Dagum Distribution: Properties and Applications
AU  - Adana’a Felix Chama
Y1  - 2021/04/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ml.20210701.12
DO  - 10.11648/j.ml.20210701.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 7
EP  - 18
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20210701.12
AB  - In this article, a generalization of the new cubic transmuted Dagum (CTD) distribution is derived and have developed a cubic transmuted family of distribution. The proposed distribution includes a special cases of the new Transmuted Dagum distribution (TDD). The objectives are to model a new distribution called cubic transmuted Dagum distribution to take care of the flexibility and multimodal (complex) effect which the transmuted form of the distribution cannot handle. The work comprises of the probability density function of cubic transmuted Dagum distribution   and its Cumulative distribution function and attempt was made to compare the new distribution with the transmuted form of the distribution. Various structural properties of the new distribution, including the moments, characteristic function, quantile, moment generating function, mean, variance, reliability analysis, order statistics are derived. The maximum likelihood estimation method has been proposed for the estimation of the parameters of the Cubic transmuted Dagum distribution. The usefulness of the derived model is illustrated using two data sets to compare the performance of the new distribution with the transmuted form of the distribution and also with the parent (Dagum) distribution, and it is proved that CTD distribution is a better distribution than the transmuted Dagum distribution and the Dagum distributions based on some goodness of fit measures. Therefore, we conclude that the new model fits real life data better than the transmuted form and the base distribution. Also cubic transmuted Dagum distribution attracts more applications in several areas such as engineering, survival data, economics and others.
VL  - 7
IS  - 1
ER  -

Copy | Download