The New Topp-Leone Exponentiated Half Logistic-Gompertz-G Family of Distributions with Applications
Keywords:
Maximum likelihood, Moments, Exponentiated-Half-Logistic Distribution, Stochastic Ordering, Gompertz Distribution, Entropy, Topp-Leone Distribution.
Abstract
This research introduces a new family of distributions (FoD) titled the Topp-Leone Exponentiated-Half-Logistic-Gompertz-G (TL-EHL-Gom-G) distribution. The study explores a variety of statistical properties of the developed family, such as the quantile function, series expansion, order statistics, entropy, stochastic orders and moments. Through Monte Carlo simulations, various estimation techniques were compared, including the least squares (LS), Anderson Darling (AD), maximum likelihood (ML) and Cram\'er-von-Mises (CVM) methods via root mean square error (RMSE) and average bias (Abias). The results indicated that the ML estimation method performed better than other methods, hence, the selection for estimating the model parameters. To showcase the usefulness, robustness and applicability of the model, we applied it to three real-life data, including dataset with censored observations. The TL-EHL-Gom-W distribution, a special case of the TL-EHL-Gom-G FoD showed superiority over nested and non-nested models.References
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Journal of Science and Technology Research, vol. 2, no. 4, pp. 83–96, 2020.
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27. Topp, C. W. and Leone, F. C., A family of J-shaped frequency functions, Journal of American Statistical Association, vol. 150, pp.
209–219, 1955.
28. Vasileva, M., Rahneva, O., Malinova, A., and Arnaudova, V., The odd Weibull-Topp-Leone-G power series family of distributions ,
International Journal of Differential Equations and Applications, vol. 20, no. 1, pp. 43–61, 2021.
29. Warahena-Liyanage, G., Oluyede, B., Moakofi, T., and Sengweni, W., The new exponentiated half logistic-Harris-G family of
distributions with actuarial measures and applications, Stats, vol. 6, no. 3, pp. 773–801, 2023.
regression modeling, properties and applications, Iranian Journal of Science and Technology, vol. 42, no. 4, pp. 2273–2288, 2018.
2. Ali, S., Dey, S,.Tahir, M.H., and Mansoor, M., The Poisson Nadarajah-Haghighi distribution: different methods of estimation,
Pakistan Journal of Statistics and Operation Research, vol. 19, no. 1, pp. 155–166, 2021.
3. 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.
4. Al-Shomrani, A., Arif, O., Shawky, A., Hanif, S., and Shahbaz, M. Q., Topp-Leone family of distributions: some properties and
application, Pakistan Journal of Statistics and Operation Research, vol. 12, no. 3 pp. 443–451, 2016.
5. Anderson, T. W., and Darling, D. A., Asymptotic theory of certain goodness-of-fit criteria based on stochastic processes, Annals of
Mathematical Statistics, vol. 23, pp. 193–212, 1952.
6. Chipepa, F., and Oluyede, B., The Topp-Leone odd exponential half logistic-G family of distributions: model properties and
applications, Pakistan Journal of Statistics, vol. 37, no. 3, pp. 253–277, 2021a.
7. Chipepa, F., and Oluyede, B., The Marshall-Olkin-Gompertz-G family of distributions: properties and applications, Journal of
Nonlinear Sciences and Applications, vol. 14, pp. 250–261, 2021b.
8. Chipepa, F., Chamunorwa, S., Oluyede, B., Makubate, B., and Zidana, C., The exponentiated half logistic-generalized-G power
series class of distributions: properties and applications, Journal of Probability and Statistical Science, vol. 20, no. 1, pp. 21–40,
2022.
9. Cordeiro, G. M., Alizadeh, M., and Ortega, E. M., The exponentiated half-logistic family of distributions: properties and applications,
Journal of Probability and Statistics, 2014.
10. Dey, S., Ali, S., and Park, C., Weighted exponential distribution: properties and different methods of estimation, Journal of Statistical
Computation and Simulation, vol. 85, no. 18 pp. 3641–3661, 2015.
11. Dingalo, N., Oluyede, B., and Chipepa, F., The Topp-Leone-Gompertz-exponentiated half logistic-G family of distributions with
applications, Revista Colombiana de Estadistica, vol. 46, no. 2, pp. 55–92, 2023.
12. Gompertz, B., On the nature of the function expressive of the law of human mortality and on the new mode of determining the value
of life contingencies, Philosophical Transactions of the Royal Statistical Society, vol. 115, pp. 513–580, 1825.
13. Khaleel, M. A., Al-Noor, N. H., and Abdal-Hameed, M. K., Marshall-Olkin exponential Gompertz distribution: properties and
applications, Periodicals of Engineering and Natural Sciences (PEN), vol. 8, no. 1 pp. 298–312, 2020.
14. Korkmaz, M. C., Yousof, H. M., and Hamedani, G. G., 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.
15. MacDonald, P., An estimation procedure for mixtures of distributions, Journal of the Royal Statistical Society, vol. 33, no. 2, pp.
102–107, 1971.
16. Moakofi, T., Oluyede, B., and Chipepa, F., The Topp-Leone half logistic generalized-G family of distributions : model, properties
and applications, EBM, vol. 4, no. 2, pp. 107–133, 2021.
17. Nanga, S., Nasiru, S., and Jakperik, D., Cosine Topp-Leone family of distributions: properties and regression, Research in
Mathematics, vol. 10, no. 1, 2023.
18. Oluyede, B., Chamunorwa, S., Chipepa, F., and Alizadeh, M., The Topp-Leone Gompertz-G family of distributions with applications,
Journal of Statistics and Management Systems, vol. 25, no. 6, pp. 1399–1423, 2022b.
19. Oluyede, B., Peter, P.O., Ndwapi, N., and Bindele, H., The exponentiated half-logistic odd burr III-G: model, properties and
applications, Pakistan Journal of Statistics and Operation Research, vol. 18, no. 1, pp. 33–57, 2022c.
20. Oluyede, B. and Moakofi, T., The Gamma-Topp-Leone-type II-exponentiated half logistic-G family of distributions with applications,
Stats, vol. 6, no. 2, pp. 706–733, 2023.
21. Oluyede, B., Dingalo, N., and Chipepa, F., The Topp-Leone-Harris-G family of distributions with applications, International Journal
of Mathematics in Operational Research (IJMOR), vol. 24, no. 4, pp. 554–581, 2023.
22. 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.
23. Sanusi, A., Doguwa, S., Isah, A., and Baraya, Y., Topp-Leone exponential-G family of distributions: properties and application,
Journal of Science and Technology Research, vol. 2, no. 4, pp. 83–96, 2020.
24. Shaked, M., and Shanthikumar, J.G., Stochastic orders, Springer, New York, 2007.
25. Shannon, C. E., Prediction and entropy of printed english, The Bell System Technical Journal, vol. 30, pp. 50–64, 1951.
26. Swain, J. J., Venkatraman, S., and Wilson, J. R., 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.
27. Topp, C. W. and Leone, F. C., A family of J-shaped frequency functions, Journal of American Statistical Association, vol. 150, pp.
209–219, 1955.
28. Vasileva, M., Rahneva, O., Malinova, A., and Arnaudova, V., The odd Weibull-Topp-Leone-G power series family of distributions ,
International Journal of Differential Equations and Applications, vol. 20, no. 1, pp. 43–61, 2021.
29. Warahena-Liyanage, G., Oluyede, B., Moakofi, T., and Sengweni, W., The new exponentiated half logistic-Harris-G family of
distributions with actuarial measures and applications, Stats, vol. 6, no. 3, pp. 773–801, 2023.
Published
2025-06-10
How to Cite
Charumbira, W., Oluyede, B., & Chipepa, F. (2025). The New Topp-Leone Exponentiated Half Logistic-Gompertz-G Family of Distributions with Applications. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2238
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Research Articles
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