Published

2024-01-01

Application of the New Extended Topp-Leone Distribution to Complete and Censored Data

Aplicación de la nueva distribución extendida Topp-Leone a datos completos y censurados

DOI:

https://doi.org/10.15446/rce.v47n1.111899

Keywords:

Gamma distribution, Type II Half Logistic Top Leone-G distribution, Order Statistics, Probability Weighted Moments, Renyi entropy (en)
Distribución gamma, Distribución Tipo II Half Logistic Top Leone-G, Estadísticas de pedidos, Momentos ponderados de probabilidad, Entropía Renyi (es)

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Authors

  • Violet Zivai Nyamajiwa Botswana International University of Science and Technology
  • Regent Retrospect Musekwa Botswana International University of Science and Technology
  • Boikanyo Makubate Botswana International University of Science & Technology https://orcid.org/0000-0002-1581-3165
One of the most important applications of statistical models is in analyzing survival data. In this study, we developed the Gamma Type Two Half Logistic Topp-Leone-G model using the technique earlier proposed by Zografos and Balakrishnan. Different characteristics of the proposed distribution are obtained. In order to estimate the model parameters based on complete and censored data, the maximum likelihood estimation method is used. Through Monte Carlo simulation, the performance of the estimators is evaluated. The proposed distribution's potential significance and applicability are empirically demonstrated using actual datasets. We found that our new distribution is a very competitive model for describing both complete and censored observations in survival analysis. The work demonstrated that in certain cases, our new model performed better than other parametric models with the same number of parameters.
Una de las aplicaciones más importantes de los modelos estadísticos es el análisis de datos de supervivencia. En este estudio, desarrollamos el modelo Gamma Tipo Dos Half Logistic Topp-Leone-G utilizando la técnica propuesta anteriormente por Zografos y Balakrishnan. Se obtienen diferentes características de la propuesta de distribución. Para estimar los parámetros del modelo a partir de datos completos y censurados se utiliza el método de estimación de máxima verosimilitud. A través de la simulación Monte Carlo se evalúa el desempeño de los estimadores. La importancia y aplicabilidad potencial de la propuesta de distribución se demuestra empíricamente utilizando conjuntos de datos reales. Descubrimos que nuestra nueva distribución es un modelo muy competitivo para describir observaciones tanto completas como censuradas en el análisis de supervivencia. El trabajo demostró que, en ciertos casos, nuestro nuevo modelo funcionó mejor que otros modelos paramétricos con la misma cantidad de parámetros.

References

Aczél, J., Forte, B. & Ng, C. T. (1974), 'Why the shannon and hartley entropies are 'natural", Advances in Applied Probability 6(1), 131-146. DOI: https://doi.org/10.2307/1426210

Adamidis, K. & Loukas, S. (1998), 'A lifetime distribution with decreasing failure rate', Statistics & Probability Letters 39(1), 35-42. DOI: https://doi.org/10.1016/S0167-7152(98)00012-1

Al-Shomrani, A., Arif, O., Shawky, A., Hanif, S. & Shahbaz, M. Q. (2016), 'Toppá Leone Family of Distributions: Some Properties and Application', Pakistan Journal of Statistics and Operation Research pp. 443-451. DOI: https://doi.org/10.18187/pjsor.v12i3.1458

Alzaatreh, A., Famoye, F. & Lee, C. (2014), 'The gamma-normal distribution: Properties and applications', Computational Statistics & Data Analysis 69, 67- 80. DOI: https://doi.org/10.1016/j.csda.2013.07.035

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

Balakrishnan, N. (1985), 'Order statistics from the half logistic distribution', Journal of statistical computation and simulation 20(4), 287-309. DOI: https://doi.org/10.1080/00949658508810784

Bantan, R. A., Jamal, F., Chesneau, C. & Elgarhy, M. (2020), 'Type II Power Topp-Leone generated family of distributions with statistical inference and applications', Symmetry 12(1), 75. DOI: https://doi.org/10.3390/sym12010075

Bosyk, G. M., Portesi, M. & Plastino, A. (2012), 'Collision entropy and optimal uncertainty', Physical Review A 85, 012108. https //link.aps.org/doi/10.1103/PhysRevA.85.012108 DOI: https://doi.org/10.1103/PhysRevA.85.012108

Chamunorwa, S., Oluyede, B., Makubate, B. & Chipepa, F. (2021), 'The exponentiated odd Weibull-Topp-Leone-G family of distributions Model, properties and applications'. DOI: https://doi.org/10.22436/jnsa.014.04.06

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

Chipepa, F., Oluyede, B., Makubate, B. et al. (2020), 'The Topp-Leone-Marshall- Olkin-G family of distributions with applications', Jnternational Journal of Statistics and Probability 9(4), 15-32. DOI: https://doi.org/10.5539/ijsp.v9n4p15

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

Elgarhy, M., Arslan Nasir, M., Jamal, F. & Ozel, G. (2018), 'The type II Topp-Leone generated family of distributions: Properties and applications', Journal of Statistics and Management Systems 21(8), 1529-1551. DOI: https://doi.org/10.1080/09720510.2018.1516725

Fagbamigbe, A. F., Basele, G. K., Makubate, B. & Oluyede, B. O. (2019), 'Appli- cation of the Exponentiated Log-Logistic Weibull Distribution to Censored Data', Journal of the Nigerian Society of Physical Sciences pp. 12-19. DOI: https://doi.org/10.46481/jnsps.2019.4

Foya, S., Oluyede, B. O., Fagbamigbe, A. F. & Makubate, B. (2017), 'The gamma log-logistic Weibull distribution: model, properties and application', Electronic Journal of Applied Statistical Analysis 10(1), 206-241.

Handique, L., Chakraborty, S. & Ali, M. M. (2023), 'The Topp-Leone-G Power Series Distribution', G Families of Probability Distributions: Theory and Practices p. 132. DOI: https://doi.org/10.1201/9781003232193-9

Hassan, A. S. & Abd-Allah, M. (2018), 'Exponentiated Weibull-Lomax distribution: properties and estimation', Journal of Data Science 16(2), 277-298. DOI: https://doi.org/10.6339/JDS.201804_16(2).0004

Henze, N. & Klar, B. (2002), 'Goodness-of-fit tests for the inverse Gaussian distribution based on the empirical Laplace transform', Annals of the Institute of Statistical Mathematics 54, 425-444. DOI: https://doi.org/10.1023/A:1022442506681

Hogg, R., McKean, J. & Craig, A. (2005), Jntroduction to Mathematical Statistics, Pearson education international, Pearson Education. https //books.google.co.bw/books?id=vIEZAQAAIAAJ

Jones, M. C. (2004), 'Families of distributions arising from distributions of order statistics', Test 13, 1-43. DOI: https://doi.org/10.1007/BF02602999

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

Kim, Y., Guyot, C. & Kim, Y.-S. (2021), 'On the effi cient estimation of min- entropy', JEEE Transactions on Jnformation Forensics and Security 16, 3013- 3025. DOI: https://doi.org/10.1109/TIFS.2021.3070424

Makubate, B., Oluyede, B. & Gabanakgosi, M. (2021), 'A New Lindley-Burr XII Distribution: Model, Properties and Applications', Jnternational Journal of Statistics and Probability 10(4), 33-51. DOI: https://doi.org/10.5539/ijsp.v10n4p33

Makubate, B., Rannona, K., Oluyede, B. & Chipepa, F. (2021), 'The topp leone-g power series class of distributions with applications', Pakistan Journal of Statistics and Operation Research 17, 827-846. DOI: https://doi.org/10.18187/pjsor.v17i4.3636

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

Nadarajah, S. & Kotz, S. (2003), 'Moments of some J-shaped distributions', Journal of Applied Statistics 30(3), 311-317. DOI: https://doi.org/10.1080/0266476022000030084

Oluyede, B. O., Makubate, B., Wanduku, D., Elbatal, I. & Sherina, V. (2017), 'The gamma-generalized inverse Weibull distribution with applications to pricing and lifetime data', Journal of Computations & Modelling 7(2), 1.

Oluyede, B., Pu, S., Makubate, B. & Qiu, Y. (2018), 'The gamma-Weibull-G family of distributions with applications ', Austrian Journal of Statistics 47(1), 45-76. DOI: https://doi.org/10.17713/ajs.v47i1.155

Ristié, M. M. & Balakrishnan, N. (2012), 'The gamma-exponentiated exponential distribution', Journal of Statistical Computation and Simulation 82(8), 1191-1206. DOI: https://doi.org/10.1080/00949655.2011.574633

Sangsanit, Y. & Bodhisuwan, W. (2016), 'The Topp-Leone generator of distributions: properties and inferences', Songklanakarin Journal of Science & Technology 38(5). DOI: https://doi.org/10.1109/ICMSA.2016.7954316

Shannon, C. E. (1948), 'A mathematical theory of communication', The Bell System Technical Journal 27(3), 379-423. DOI: https://doi.org/10.1002/j.1538-7305.1948.tb01338.x

Soliman, A. H., Elgarhy, M. A. E. & Shakil, M. (2017), 'Type II half logistic family of distributions with applications', Pakistan Journal of Statistics and Operation Research pp. 245-264. DOI: https://doi.org/10.18187/pjsor.v13i2.1560

Tahir, M. H., Cordeiro, G. M., Mansoor, M. & Zubair, M. (2015), 'The Weibull-Lomax distribution: properties and applications', Hacettepe Journal of Mathematics and Statistics 44(2), 455-474. DOI: https://doi.org/10.15672/HJMS.2014147465

Topp, C. W. & Leone, F. C. (1955), 'A family of J-shaped frequency functions', Journal of the American Statistical Association 50(269), 209-219. DOI: https://doi.org/10.1080/01621459.1955.10501259

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

Nyamajiwa, V. Z., Musekwa, R. R. and Makubate, B. (2024). Application of the New Extended Topp-Leone Distribution to Complete and Censored Data. Revista Colombiana de Estadística, 47(1), 37–65. https://doi.org/10.15446/rce.v47n1.111899

ACM

[1]
Nyamajiwa, V.Z., Musekwa, R.R. and Makubate, B. 2024. Application of the New Extended Topp-Leone Distribution to Complete and Censored Data. Revista Colombiana de Estadística. 47, 1 (Jan. 2024), 37–65. DOI:https://doi.org/10.15446/rce.v47n1.111899.

ACS

(1)
Nyamajiwa, V. Z.; Musekwa, R. R.; Makubate, B. Application of the New Extended Topp-Leone Distribution to Complete and Censored Data. Rev. colomb. estad. 2024, 47, 37-65.

ABNT

NYAMAJIWA, V. Z.; MUSEKWA, R. R.; MAKUBATE, B. Application of the New Extended Topp-Leone Distribution to Complete and Censored Data. Revista Colombiana de Estadística, [S. l.], v. 47, n. 1, p. 37–65, 2024. DOI: 10.15446/rce.v47n1.111899. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/111899. Acesso em: 28 mar. 2025.

Chicago

Nyamajiwa, Violet Zivai, Regent Retrospect Musekwa, and Boikanyo Makubate. 2024. “Application of the New Extended Topp-Leone Distribution to Complete and Censored Data”. Revista Colombiana De Estadística 47 (1):37-65. https://doi.org/10.15446/rce.v47n1.111899.

Harvard

Nyamajiwa, V. Z., Musekwa, R. R. and Makubate, B. (2024) “Application of the New Extended Topp-Leone Distribution to Complete and Censored Data”, Revista Colombiana de Estadística, 47(1), pp. 37–65. doi: 10.15446/rce.v47n1.111899.

IEEE

[1]
V. Z. Nyamajiwa, R. R. Musekwa, and B. Makubate, “Application of the New Extended Topp-Leone Distribution to Complete and Censored Data”, Rev. colomb. estad., vol. 47, no. 1, pp. 37–65, Jan. 2024.

MLA

Nyamajiwa, V. Z., R. R. Musekwa, and B. Makubate. “Application of the New Extended Topp-Leone Distribution to Complete and Censored Data”. Revista Colombiana de Estadística, vol. 47, no. 1, Jan. 2024, pp. 37-65, doi:10.15446/rce.v47n1.111899.

Turabian

Nyamajiwa, Violet Zivai, Regent Retrospect Musekwa, and Boikanyo Makubate. “Application of the New Extended Topp-Leone Distribution to Complete and Censored Data”. Revista Colombiana de Estadística 47, no. 1 (January 24, 2024): 37–65. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/111899.

Vancouver

1.
Nyamajiwa VZ, Musekwa RR, Makubate B. Application of the New Extended Topp-Leone Distribution to Complete and Censored Data. Rev. colomb. estad. [Internet]. 2024 Jan. 24 [cited 2025 Mar. 28];47(1):37-65. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/111899

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CrossRef citations4

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

2. Regent Retrospect Musekwa, Boikanyo Makubate. (2024). A flexible generalized XLindley distribution with application to engineering. Scientific African, 24, p.e02192. https://doi.org/10.1016/j.sciaf.2024.e02192.

3. Regent Retrospect Musekwa, Lesego Gabaitiri, Boikanyo Makubate. (2024). Application of the Marshall-Olkin-Weibull logarithmic distribution to complete and censored data. Heliyon, 10(14), p.e34170. https://doi.org/10.1016/j.heliyon.2024.e34170.

4. Boikanyo Makubate, Difang Huang. (2024). A Test for Discriminating Between Members of the Odd Weibull‐G Family of Distributions. The Scientific World Journal, 2024(1) https://doi.org/10.1155/2024/9423417.

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