The Marshall-Olkin-Topp-Leone-Gompertz-G Family of Distributions with Applications
Keywords:
Marshall-Olkin-G, Topp-Leone-Gompertz-G, Maximum Likelihood Estimation
Abstract
A new family of distributions called the Marshall-Olkin-Topp-Leone-Gompertz-G (MO-TL-Gom-G) distribution is developed and studied in detail. Some mathematical and statistical properties of the new family of distributions are explored. Statistical properties of the new family of distributions considered are the quantile function, moments and generating function, probability weighted moments, distribution of the order statistics and R\'enyi entropy. The maximum likelihood technique is used for estimating the model parameters and Monte Carlo simulation is conducted to examine the performance of the model. Finally, we give examples of real-life data applications to show the usefulness of the above mentioned Topp-Leone-Gompertz generalization.References
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29. Oluyede, B. O., Chamunorwa, S., Chipepa, F. and Alizadeh, M., The Topp-Leone Gompertz-G family of distributions with
applications, Journal of Statistics & Management Systems, (To appear) 2022.
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vol. 13, no. 2, pp. 241–260, 2021.
Regression modeling, properties, and applications, Iranian Journal of Science and Technology, Transactions A: Science, vol. 42, no.
4, pp. 2273–2288, 2018.
2. Alizadeh, M., Cordeiro, G. M., Pinho, L. G. B. and Ghosh, I., The Gompertz-G family of distributions, Journal of Statistical Theory
and Practice, vol. 11, no. 1, pp. 179–207, 2017.
3. Alizadeh, M., Cordeiro, G. M., Brito, E. and Dem´etrio, C. G., The beta Marshall-Olkin family of distributions, Journal of Statistical
Distributions and Applications, vol. 4, no. 2, pp. 1–18, 2015a.
4. Alizadeh, M., Emadi, M., Doostparast, M., Cordeiro, G. M., Ortega, E. and Pescim, R., A new family of distributions: The
Kumaraswamy odd log-logistic, properties and applications, Hacettepe Journal of Mathematics and Statistics, vol. 44, pp. 1491—
1512, 2015b.
5. Aryal, G. R., Ortega, E. M., Hamedani, G. G. and Yousof, H. M., The Topp-Leone generated Weibull distribution: regression model,
characterizations and applications, International Journal of Statistics and Probability, vol. 6, no. 1, pp. 126–141, 2017.
6. Barlow, R. E., Toland, R. H. and Freeman, T., A Bayesian analysis of stress-rupture life of kevlar 49/epoxy spherical pressure vessels,
In Proc. Conference on Applications of Statistics, Marcel Dekker, New York, 1984.
7. Barreto-Souza, W., Lemonte, A. J. and Cordeiro, G. M., General results for the Marshall and Olkin’s family of distributions, Anais
da Academia Brasileira de Ci´encias, vol. 85, no. 1, pp. 3–21, 2013.
8. Benkhelifa, L., The Marshall-Olkin extended generalized gompertz distribution Journal of Data Science, vol. 15, no. 2, pp. 239–266,
2017.
9. Chakraborty, S. and Handique, L., The generalized Marshall Olkin-Kumaraswamy-G family of distributions, Journal of Data Science,
vol. 15, no. 3, pp. 391–422, 2017.
10. Chambers, J., Cleveland, W., Kleiner, B. and Tukey, J., Graphical methods for data analysis, Chapman and Hall, London, 1983.
11. Chen, G. and Balakrishnan, N., A general purpose approximate goodness-of-fit test, Journal of Quality Technology, vol. 27, pp.
154–161, 1995.
12. Chipepa, F. and Oluyede, B., The Marshall-Olkin-Gompertz-G family of distributions: properties and applications, Journal of
Nonlinear Sciences & Applications (JNSA), vol. 14, no. 4, pp. 250–267, 2021.
13. Chipepa, F., Oluyede, B. and Makubate, B., The Topp-Leone-Marshall-Olkin-G family of distributions with applications,
International Journal of Statistics and Probability, vol. 9, no. 4, pp. 15–32, 2020.
14. El-Damcese, M. A., Mustafa, A., El-Desouky, B. S. and Mustafa, M. E. The odd generalized exponential Gompertz distribution,
Applied Mathematics, vol. 6, pp. 2340–2353, 2015.
15. El-Damcese, M. A., Mustafa, A. and Eliwa, M. S., Exponentiated generalized Weibull Gompertz distribution arXiv preprint
arXiv:1412.0705, 2014.
16. Gompertz, B., On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value
of life contingencies, Philosophical Transactions of the Royal Society of London, vol. 115, pp. 513–583, 1825.
17. Greenwood, J. A., Landwehr, J. M., Matalas, N. C. and Wallis, J. R., Probability weighted moments: definition and relation to
parameters of several distributions expressible in inverse form, Water Resources Research, vol. 15, no. 5, pp. 1049–1054, 1979.
18. Gross, A. J. and Clark, V., Survival distributions: reliability applications in the biomedical sciences. John Wiley & Sons, 1975.
19. Jafari, A. A., Tahmasebi, S. and Alizadeh, M., The beta-Gompertz distribution, Revista Colombiana de Estadi´stica, vo. 37, no. 1,
141-158, 2014.
20. Karamikabir, H., Afshari, M., Alizadeh, M. and Hamedani, G. G., A new extended generalized Gompertz distribution with statistical
properties and simulations, Communications in Statistics-Theory and Methods, vol. 50, no. 2, pp. 251–279, 2021.
21. Kumagai, S. and Matsunaga, I., Physiologically based pharmacokinetic model for acetone Occupational and Environmental
Medicine, vol. 52, no. 5, pp. 344–352, 1995.
22. Kumar, D., Ratio and inverse moments of Marshall-Olkin extended Burr type III distribution based on lower generalized order
statistics, Journal of Data Science, vol. 14, no. 1, pp. 53–66, 2016.
23. Lazhar, B. Marshall-Olkin extended generalized Gompertz distribution, Journal of Data Science, vol. 15, no. 2, pp. 239-–266,
2017.
24. Lee, E. T. and Wang, J., Statistical methods for survival data analysis, Vol. 476, John Wiley & Sons, 2003.
25. Lepetu, L., Oluyede, B. O., Makubate, B., Foya, S. and Mdlongwa, P., Marshall-Olkin log-logistic extended Weibull distribution:
theory, properties and applications, Journal of Data Science, vol. 15, pp. 691–722, 2017.
26. Makubate, B., Chipepa, F, Oluyede, B. and Peter, O. P., The Marshall-Olkin Half Logistic-G family of distributions with applications,
International Journal of Statistics and Probability, vol. 10, no. 2, pp. 120–137, 2021.
27. Marshall, A. W. and Olkin, I., A new method for adding a parameter to a family of distributions with application to the exponential
and Weibull families, Biometrika, vol. 84, no. 3, pp. 641–652, 1997.
28. Nzei, L. C., Eghwerido, J. T. and Ekhosuehi, N., Topp-Leone Gompertz distribution: properties and applications, Journal of Data
Science, vol. 18, no. 4, pp. 782–794, 2020.
29. Oluyede, B. O., Chamunorwa, S., Chipepa, F. and Alizadeh, M., The Topp-Leone Gompertz-G family of distributions with
applications, Journal of Statistics & Management Systems, (To appear) 2022.
30. R´enyi, A., On measures of entropy and information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics
and Probability, vol. 1, pp. 547–561, 1960.
31. Shaked, M. Shanthikumar, J. G., Stochastic orders, Springer, New York, 2007.
32. Silva, R. C. D., Sanchez, J. J., Lima, F. P. and Cordeiro, G. M., The Kumaraswamy Gompertz distribution, Journal of Data Science,
vol. 13, no. 2, pp. 241–260, 2021.
Published
2024-04-13
How to Cite
Oluyede, B., Gabanakgosi, M., & Warahena-Liyanage, G. (2024). The Marshall-Olkin-Topp-Leone-Gompertz-G Family of Distributions with Applications. Statistics, Optimization & Information Computing, 12(4), 882-906. https://doi.org/10.19139/soic-2310-5070-1509
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Research Articles
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