The New Topp-Leone-Marshall-Olkin-Gompertz-G Family of Distributions: Properties, Different Estimation Techniques and Applications on Censored and Complete Data
Keywords:
Gompertz-G distribution, Marshall-Olkin-G distribution, maximum likelihood estimation, least squares, weighted least squares, Anderson Darling, Cramer-von Mises, likelihood ratio test
Abstract
A new family of distributions (FoD) called the Topp-Leone-Marshall-Olkin Gompertz-G is presented in this paper. Derivations of some statistical properties were carried out. The model parameters were estimated using five methods, including weighted least squares, maximum likelihood estimation, least squares, Cram\'er-von Mises, and Anderson Darling. The simulation experiment assessed the precision of the model parameters through the utilization of five estimation methods. To evaluate the adaptability and utility of this new FoD, three real-life datasets were analyzed using a special case from the developed family of distributions, one of which contained censored data. Remarkably, the new model showed exceptional performance when compared against six other non-nested models. This comparison highlighted its superiority and effectiveness in modeling real-life datasets.References
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2. H. H. Ahmad, O. M. Bdair, and M. A. Ahsanullah, On Marshall-Olkin Extended Weibull Distribution, Journal of Statistical Theory
and Applications, vol. 16, no. 1, pp. 1–17, 2017.
3. M. Aldahlan, and A. Z. Afify, The Odd Exponentiated Half-Logistic Burr XII Distribution, Pakistan Journal of Statistics and
Operation Research, vol. 14, no. 2, pp. 317–329, 2018.
4. M. Alizadeh, L. Benkhelifa, M. Rasekhi, and B. Husseini, The Odd Log -Logistic Generalised Gompertz Distribution: Properties,
Applications and Different Methods of Estimation, Communications in Mathematics and Statistics, vol. 8, no. 1, pp. 295– 317, 2020.
5. W. Barreto-Souza, H. S. and Bakouch, A New Lifetime Model with Decreasing Failure Rate, Statistics, vol. 47, no. 6, pp. 465–476,
2013.
6. W. Barreto-Souza, J. A. Lemonte, and G. M. Cordeiro, General Results for the Marshall and Olkin’s Family of Distributions, Anais
da Academia Brasileira de Ciencias, vol. 2, no. 3, pp. 3–21, 2013.
7. M. Bourguignon, R. B. Silva, and G. M. Cordeiro, The Weibull-G Family of Probability Distributions, Journal of Data Science, vol.
12, pp. 53–68, 2014.
8. E. Brito, G. M. Cordeiro, H. M. Yousof,M. Alizadeh, and G. O Silva, The Topp-Leone Odd Log Logistic Family of Distributions,
Journal of Statistical Computation and Simulation, vol. 87, no. 15, pp. 3040–3058, 2017.
9. F. Chipepa, B. Oluyede, and B. Mukubate, The Topp-Leone Marshall-Olkin-G Family of Distributions with Applications,
International Journal of Statistics and Probability, vol. 9, no. 4, pp. 1-15, 2020.
10. F. Chipepa, and B. Oluyede, The Marshall-Olkin-Gompertz-G Family of Distributions: Properties and Applications, Journal of
Nonlinear Sciences and Applications, vol. 14, pp. 250–267, 2021.
11. J. U. Cleaton, and S. D. Lynch, Properties of Generalised Log-Logistic Families of Lifetime Distributions, Journal of Probability
and Statistical Science, vol. 4, no. 1, pp. 52–64, 2006.
12. G. M. Cordeiro, E. M. M. Ortega, and S. Nadarajaah, The Kumaraswamy Weibull Distribution with Application to Failure Data,
Journal of the Franklin Institute, vol. 347, no. 6, pp. 1399–1429, 2010.
13. G. M. Cordeiro, M. Alizadeh, A. D. C. Nascimento, and M. Rasekhi, The Exponentiated Gompertz Generated Family of
Distributions: Properties and Applications, Chilean Journal of Statistics, vol. 7, no. 1, pp. 29–50, 2016.
14. A. El-Gohary, A. Alshamrani, and A. Al-Otaili, The Generalized Gompertz Distribution, Applied Mathematical Modelling, vol. 37,
pp. 13–24, 2013.
15. M. Elgarhy, M. Shakil, and B. M. Golam Kibria, Exponentiated Weibull-Exponential Distribution with Applications, Applications
and Applied Mathematics: An International Journal, vol. 12, no. 2, pp. 710–725, 2017.
16. E.A.A. Hassan, M. Elgarhy, E.A Eldessouky, O.H.M. Hassan, E.A. Amin, and E.M Almetwally, Different Estimation Methods for
New Probability Distribution Approach Based on Environmental and Medical Data, Axioms, vol. 12, no. 2, pp. 1–24, 2023.
17. A. A. Jafari, S. Tahmasebi, and M. Alizadeh, The Beta Gompertz Distribution, Revista Colombiana de Estad´ıstica, vol. 37, no. 1,
pp. 141–158, 2014.
18. H.S. Klakattawi, Survival Analysis of Cancer Patients Using a New Extended Weibull Distribution, PLoS ONE, vol. 17, no. 2, pp.
26–42, 2022.
19. M.C. Korkmaz, H.M. Yousof, and G.G. Hamedani, The Exponential Lindley Odd Log-Logistic-G Family: Properties,
Characterizations and Applications, Journal of Statistical Theory and Applications, vol. 17, no. 3, pp. 554 –571, 2018.
20. J. F. Lawless, Statistical Models and Methods for Lifetime Data, 2
nd edition, John Wiley and Sons, New Jersey, 2003.
21. E.T. Lee, and J. Wang, Statistical Methods for Survival Data Analysis, John Wiley Sons, Incorporated, DOI:10.1002/0471458546,
2003.
22. P.A.W. Lewis, Distribution of the Anderson-Darling Statistic, The Annals of Mathematical Statistics, vol. 32, no. 4, pp. 1118–1124,
1961.
23. W. A. Marshall, and I. Olkin, A new Method for Adding a Parameter in a Family of Distributions with Applications to the
Exponentiated and Weibull families, Biometrika, vol. 84, pp. 641–652, 1997.
24. T. Moakofi, B. Oluyede, and M. Gabanakgosi, The Topp-Leone Odd Burr III-G Family of Distributions: Model, Properties and
Applications, Journal of Statistics, Optimization and Information Computing, vol. 10, pp. 236–262, 2022.
25. B. Oluyede, S. Chamunorwa, F. Chipepa, and M. Alizadeh, The Topp-Leone Gompertz-G Family of Distributions with Applications,
Journal of Statistics and Management Systems, vol. 25, no. 6, pp. 1399-1423, 2022.
26. A. Renyi, , ´ On Measures of Entropy and Information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics
and Probability, vol. 4, no. 1, pp. 547–561, 1960.
27. M. Shaked, and J.G. Shanthikumar, Stochastic Orders, Springer Science and Business Media, pp. 3 - 473, 2007.
28. Y. Sangsanit, and W. Bodhisuwan, The Topp-Leone Generator of Distributions: Properties and Inferences, Journal of Science and
Technology, vol. 38, no. 5, pp. 537–548, 2016.
29. C. E. Shannon, Prediction and Entropy of Printed English, The Bell System Technical Journal, vol. 30, no. 1, pp. 50-64, 1951.
30. J.J. Swain, S. Venkatraman, and J.R. Wilson, Least-Squares Estimation of Distribution Functions in Johnson’s Translation System,
Journal of Statistical Computation and Simulation, vol. 29, no. 4, pp. 271—297, 1988.
31. Q.M. William, and L.A Escobar, Statistical Methods for Reliability Data, A. Wiley Interscience Publications, pp. 639, 1998.
32. K. Zografos, and N., Balakrishnan, On Families of Beta and Generalised Gamma Generalised Distributions and Associated
Inference, Statistical Methodology Journal, vol. 6, no. 1, pp. 344–362, 2009.
Published
2025-04-05
How to Cite
Chinofunga, P. T., Oluyede, B., & Chipepa, F. (2025). The New Topp-Leone-Marshall-Olkin-Gompertz-G Family of Distributions: Properties, Different Estimation Techniques and Applications on Censored and Complete Data. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2239
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Research Articles
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