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.

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How to Cite

APA

Musekwa, R. R., Gabaitiri, L. and 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: 30 jan. 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 January 30, 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 Jan. 30];47(2):329-54. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/112245

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