Published

2024-07-01

A New Technique to Generate Families of Continuous Distributions

Una nueva técnica para generar familias de distribuciones continuas

DOI:

https://doi.org/10.15446/rce.v47n2.112245

Keywords:

Alpha-Power transformation, Alpha-Power transformed-G, Goodness-of-fit statistics, Maximum Likelihood estimation, Power distribution (en)
Alfa-Poder Transformado-G, Distribución de poder, Estadísticas de bondad de ajuste, Estimación de máxima verosimilitud, Transformación de poder alfa (es)

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Authors

  • Regent Retrospect Musekwa University of Science and Technology
  • Lesego Gabaitiri University of Science and Technology
  • Boikanyo Makubate University of Science and Technology

We introduce a novel technique for producing several families of distributions: the alpha-log-power transformed method. The novelty of our new approach lies in the fact that it adds one new shape parameter and was not derived from any established parent model. Some examples of the new family are presented. Also, some important statistical properties of the new family are studied. The maximum likelihood estimation approach is utilized to estimate the model parameters of the new family. To evaluate the performance of the estimators, Monte Carlo simulation is conducted using some arbitrary baseline distributions namely the Weibull, Burr-XII and Pareto distribution. Two real datasets are used to empirically show the potential significance and applicability of the alpha log power transformed Weibull. The alpha log power transformed Weibull is a very competitive model for characterizing observations in survival analysis.

Introducimos una técnica novedosa para producir varias familias de distribuciones: el método transformado de potencia logarítmica alfa. La novedad de nuestro nuevo enfoque radica en el hecho de que agrega un nuevo parámetro de forma y no se deriva de ningún modelo principal establecido. Se presentan algunos ejemplos de la nueva familia. Además, se estudian algunas propiedades estadísticas importantes de la nueva familia. Se utiliza el enfoque de estimación de máxima verosimilitud para estimar los parámetros del modelo de la nueva familia. Para evaluar el desempeño de los estimadores, se realiza una simulación de Monte Carlo utilizando algunas distribuciones de referencias arbitrarias, a saber, la distribución de Weibull, Burr-XII y Pareto. Se utilizan dos conjuntos de datos reales para mostrar empíricamente la importancia potencial y la aplicabilidad de Weibull transformado en potencia logarítmica alfa. El poder logarítmico alfa transformado de Weibull es un modelo muy competitivo para caracterizar observaciones en el análisis de supervivencia.

References

Ahmad, A., Ahmad, S. & Ahmed, A. (2014), 'Transmuted inverse rayleigh distribution: A generalization of the inverse rayleigh distribution', Mathematical Theory and Modeling 4(7), 90_98.

Alamatsaz, M., Dey, S., Dey, T. & Harandi, S. S. (2016), 'Discrete generalized rayleigh distribution', Pakistan Journal of Statistics 32(1).

Ali, M., Khalil, A., Ijaz, M. & Saeed, N. (2021), 'Alpha-power exponentiated inverse rayleigh distribution and its applications to real and simulated data', PloS One 16(1), e0245253. DOI: https://doi.org/10.1371/journal.pone.0245253

Alzaatreh, A., Lee, C. & Famoye, F. (2013), 'A new method for generating families of continuous distributions', Metron 71(1), 63_79. DOI: https://doi.org/10.1007/s40300-013-0007-y

Bourguignon, M., Silva, R. B. & Cordeiro, G. M. (2014), 'The weibull-g family of probability distributions', Journal of Data Science 12(1), 53_68. DOI: https://doi.org/10.6339/JDS.201401_12(1).0004

Chen, G. & Balakrishnan, N. (1995), 'A general purpose approximate goodness of-fit test', Journal of Quality Technology 27(2), 154_161. DOI: https://doi.org/10.1080/00224065.1995.11979578

Cleveland, W. S. & McGill, R. (1984), 'Graphical perception: Theory, experimentation, and application to the development of graphical methods', Journal of the American Statistical Association 79(387), 531_554. DOI: https://doi.org/10.1080/01621459.1984.10478080

Cooray, K. (2010), 'Generalized gumbel distribution', Journal of Applied Statistics 37(1), 171_179. DOI: https://doi.org/10.1080/02664760802698995

Cordeiro, G. M., Ortega, E. M. & da Cunha, D. C. (2013), 'The exponentiated generalized class of distributions', Journal of Data Science 11(1), 1_27. DOI: https://doi.org/10.6339/JDS.201301_11(1).0001

Dey, S., Al-Zahrani, B. & Basloom, S. (2017), 'Dagum distribution: Properties and different methods of estimation', International Journal of Statistics and Probability 6(2), 74_92. DOI: https://doi.org/10.5539/ijsp.v6n2p74

Eugene, N., Lee, C. & Famoye, F. (2002), 'Beta-normal distribution and its applications', Communications in Statistics-Theory and Methods 31(4), 497_512. DOI: https://doi.org/10.1081/STA-120003130

Gradshteyn, I. S. & Ryzhik, I. M. (2014), Table of integrals, series, and products, Academic press.

Granzotto, D., Louzada, F. & Balakrishnan, N. (2017), 'Cubic rank transmuted distributions: inferential issues and applications', Journal of Statistical Computation and Simulation 87(14), 2760_2778. DOI: https://doi.org/10.1080/00949655.2017.1344239

Gupta, R. C., Gupta, P. L. & Gupta, R. D. (1998), 'Modeling failure time data by lehman alternatives', Communications in Statistics-Theory and Methods 27, 887_904. https://api.semanticscholar.org/CorpusID:121377222 DOI: https://doi.org/10.1080/03610929808832134

Keganne, K., Gabaitiri, L. & Makubate, B. (2023), 'A new extension of the exponentiated generalized-G family of distributions', Scientific African 20, e01719. https://www.sciencedirect.com/science/article/pii/S2468227623001758 DOI: https://doi.org/10.1016/j.sciaf.2023.e01719

Liu, X., Ahmad, Z., Gemeay, A. M., Abdulrahman, A. T., Hafez, E. & Khalil, N. (2021), 'Modeling the survival times of the COVID-19 patients with a new statistical model: A case study from china', PloS One 16(7), e0254999. DOI: https://doi.org/10.1371/journal.pone.0254999

Mahdavi, A. & Kundu, D. (2017), 'A new method for generating distributions with an application to exponential distribution', Communications in Statistics-Theory and Methods 46(13), 6543_6557. DOI: https://doi.org/10.1080/03610926.2015.1130839

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(3), 641_652. DOI: https://doi.org/10.1093/biomet/84.3.641

Musekwa, R. R. & Makubate, B. (2023), 'Statistical analysis of saudi arabia and uk covid-19 data using a new generalized distribution', Scientific African 22, e01958. https://www.sciencedirect.com/science/article/pii/S2468227623004131 DOI: https://doi.org/10.1016/j.sciaf.2023.e01958

Musekwa, R. R. & Makubate, B. (2024), 'A flexible generalized xlindley distribution with application to engineering', Scienti_c African p. e02192. DOI: https://doi.org/10.1016/j.sciaf.2024.e02192

Nyamajiwa, V. Z., Musekwa, R. R. & Makubate, B. (2024), 'Application of the new extended topp-leone distribution to complete and censored data', Revista Colombiana de Estadística 47(1), 37_65. DOI: https://doi.org/10.15446/rce.v47n1.111899

Rényi, A. (1961), On measures of entropy and information, in 'Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics', Vol. 4, University of California Press, pp. 547_562.

Rinne, H. (2008), The Weibull distribution: a handbook, CRC press. Shannon, C. E. (1951), 'Prediction and entropy of printed english', Bell system technical journal 30(1), 50_64. DOI: https://doi.org/10.1002/j.1538-7305.1951.tb01366.x

Shaw, W. T. & Buckley, I. R. (2009), 'The alchemy of probability distributions: Beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map', arXiv preprint arXiv:0901.0434 .

Tahir, M., Hussain, M. A. & Cordeiro, G. M. (2022), 'A new flexible generalized family for constructing many families of distributions', Journal of Applied Statistics 49(7), 1615_1635. DOI: https://doi.org/10.1080/02664763.2021.1874891

Zimmer, W. J., Keats, J. B. & Wang, F. (1998), 'The Burr XII distribution in reliability analysis', Journal of Quality Technology 30(4), 386_394. DOI: https://doi.org/10.1080/00224065.1998.11979874

Zografos, K. & Balakrishnan, N. (2009), 'On families of beta-and generalized gamma-generated distributions and associated inference', Statistical methodology 6(4), 344_362. DOI: https://doi.org/10.1016/j.stamet.2008.12.003

How to Cite

APA

Musekwa, R. R., Gabaitiri, L. & Makubate, B. (2024). A New Technique to Generate Families of Continuous Distributions. Revista Colombiana de Estadística, 47(2), 329–354. https://doi.org/10.15446/rce.v47n2.112245

ACM

[1]
Musekwa, R.R., Gabaitiri, L. and Makubate, B. 2024. A New Technique to Generate Families of Continuous Distributions. Revista Colombiana de Estadística. 47, 2 (Jul. 2024), 329–354. DOI:https://doi.org/10.15446/rce.v47n2.112245.

ACS

(1)
Musekwa, R. R.; Gabaitiri, L.; Makubate, B. A New Technique to Generate Families of Continuous Distributions. Rev. colomb. estad. 2024, 47, 329-354.

ABNT

MUSEKWA, R. R.; GABAITIRI, L.; MAKUBATE, B. A New Technique to Generate Families of Continuous Distributions. Revista Colombiana de Estadística, [S. l.], v. 47, n. 2, p. 329–354, 2024. DOI: 10.15446/rce.v47n2.112245. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/112245. Acesso em: 28 dec. 2025.

Chicago

Musekwa, Regent Retrospect, Lesego Gabaitiri, and Boikanyo Makubate. 2024. “A New Technique to Generate Families of Continuous Distributions”. Revista Colombiana De Estadística 47 (2):329-54. https://doi.org/10.15446/rce.v47n2.112245.

Harvard

Musekwa, R. R., Gabaitiri, L. and Makubate, B. (2024) “A New Technique to Generate Families of Continuous Distributions”, Revista Colombiana de Estadística, 47(2), pp. 329–354. doi: 10.15446/rce.v47n2.112245.

IEEE

[1]
R. R. Musekwa, L. Gabaitiri, and B. Makubate, “A New Technique to Generate Families of Continuous Distributions”, Rev. colomb. estad., vol. 47, no. 2, pp. 329–354, Jul. 2024.

MLA

Musekwa, R. R., L. Gabaitiri, and B. Makubate. “A New Technique to Generate Families of Continuous Distributions”. Revista Colombiana de Estadística, vol. 47, no. 2, July 2024, pp. 329-54, doi:10.15446/rce.v47n2.112245.

Turabian

Musekwa, Regent Retrospect, Lesego Gabaitiri, and Boikanyo Makubate. “A New Technique to Generate Families of Continuous Distributions”. Revista Colombiana de Estadística 47, no. 2 (July 12, 2024): 329–354. Accessed December 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/112245.

Vancouver

1.
Musekwa RR, Gabaitiri L, Makubate B. A New Technique to Generate Families of Continuous Distributions. Rev. colomb. estad. [Internet]. 2024 Jul. 12 [cited 2025 Dec. 28];47(2):329-54. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/112245

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