Development of Exponentiated Cosine Topp-Leone Generalized Family of Distributions and its Applications to Lifetime Data
DOI:
https://doi.org/10.56919/usci.2431.017Keywords:
Cosine Generalized family, Exponentiated Generalized family, Topp-Leone distribution, moments, parameter estimationAbstract
The Topp-Leone distribution is widely used for modeling lifetime data across many disciplines. This paper presents the Exponentiated Cosine Topp-Leone Generalized family (ExCTLG), which is an extension of the Topp-Leone family. The research examines the mathematical properties of the ExCTLG, including the survival and hazard functions, moments, moment-generating functions, and Renyi’s entropy. Parameter estimation is carried out using the maximum likelihood estimation (MLE) techniques, and the estimated parameters consistency is validated using the Monte Carlo simulation method, thereby highlighting the superiority of MLE. The advantages and applicability of the proposed distribution are shown by analyzing two-lifetime datasets.
References
Al-noor, N. H., & Hilal, O. A. (2021). Truncated Exponential Topp Leone Exponential Distribution : Properties and Applications. Journal of Physics: Conference Series, 1879. https://doi.org/10.1088/1742-6596/1879/3/032039
Al-saiary, Z. A., & Al-jadaani, S. H. (2022). Distribution with Real Data Applications The Type II Topp-Leone Generalized Inverted Exponential Distribution. Asian Journal of Probability and Statistics, 16(2), 37–51. https://doi.org/10.9734/AJPAS/2022/v16i230400
Al-shomrani, A. (2022). Some mathematical properties of Odd Kappa-G family. Research in Mathematics, 9(1), 1–13. https://doi.org/10.1080/27684830.2022.2095091
Chamunorwa, S., Oluyede, B., Makubate, B., & Chipepa, F. (2021). The exponentiated odd weibull-topp-leone-g family of distributions: Model, properties and applications. Pakistan Journal of Statistics, 37(2), 143–158.
Chipepa, F., & Oluyede, B. (2021). The topp-leone odd exponential half logistic-g family of distributions: Model, properties and applications. Pakistan Journal of Statistics, 37(3), 253–277.
El-morshedy, M., Eliwa, M. S., & Afify, A. Z. (2020). The Odd Chen Generator of Distributions : Properties and Estimation Methods with Applications in Medicine and Engineering. J. Natn. Sci. Foundation, 48(2), 113–130. https://doi.org/10.4038/jnsfsr.v48i2.8790
Gradshteyn, I. S., & Ryzhik, I. M. (2007). Table of integrals, series, and products: Seventh edition. In TAcademic Press is an imprint of Elsevier.
Gupta, R. D., & Kundu, D. (1999). Generalized exponential distributions r. Austral. & NewZealand J. Statist., 41(2), 173–188.
Hassan, A. S., Al-omari, A. I., Hassan, R. R., & Alomani, G. A. (2022). Journal of Radiation Research and Applied Sciences The odd inverted Topp Leone – H family of distributions : Estimation and applications. Journal of Radiation Research and Applied Sciences, 15(3), 365–379. https://doi.org/10.1016/j.jrras.2022.08.006
Ibrahim, S., Doguwa, S. I., Audu, I., & Muhammad, J. H. (2020). On the Topp Leone Exponentiated-G Family of Distributions : Properties and On the Topp Leone Exponentiated-G Family of Distributions : Properties and Applications. Asian Journal of Probability and Statistics, 7(1), 1–15. https://doi.org/10.9734/AJPAS/2020/v7i130170
Muhammad, M., Bantan, R. A. R., Liu, L., Chesneau, C., Tahir, M. H., Jamal, F., & Elgarhy, M. (2021). A new extended cosine—g distributions for lifetime studies. Mathematics, 9(21), 1–29. https://doi.org/10.3390/math9212758
Nanga, S., Nasiru, S., & Dioggban, J. (2022). Tangent Topp-Leone Family of Distributions. Scientific African, 17, e01363. https://doi.org/10.1016/j.sciaf.2022.e01363
Nanga, S., Nasiru, S., & Dioggban, J. (2023). Cosine Topp – Leone family of distributions : Properties and Regression. Research in Mathematics, 10(1). https://doi.org/10.1080/27684830.2023.2208935
Owoloko, E. A., Oguntunde, P. E., & Adejumo, A. O. (2015). Performance rating of the transmuted exponential distribution: an analytical approach. SpringerPlus, 4(1), 1–15. https://doi.org/10.1186/s40064-015-1590-6
Ramos, P. L., Louzada, F., Ramos, E., & Dey, S. (2020). The Fréchet distribution: Estimation and application - An overview. Journal of Statistics and Management Systems, 23(3), 549–578. https://doi.org/10.1080/09720510.2019.1645400
Renyi, A. (1961). ON MEASURES OF ENTROPY AND INFORMATION. Berkeley Symp. on Math. Statist. and Prob., 547–561.
Reyad, H. M., Alizadeh, M., Jamal, F., Othman, S., & Hamedani, G. G. (2019). The exponentiated generalized Topp Leone-G family of distributions: Properties and applications. Pakistan Journal of Statistics and Operation Research, 15(1), 1–24. https://doi.org/10.18187/pjsor.v15i1.2166
Sangsanit, Y., & Bodhisuwan, W. (2016). The Topp-Leone generator of distributions : properties and inferences. Songklanakarin J. Sci. Technol., 38(5), 537–548.
Souza, L., de Oliveira, W. R., de Brito, C. C. R., Chesneau, C., Fernandes, R., & Ferreira, T. A. E. (2022). Sec-G Class of Distributions: Properties and Applications. Symmetry, 14(2), 1–25. https://doi.org/10.3390/sym14020299
Souza, L., Júnior, W. R. de O., de Brito, C. C. R., Chesneau, C., Fernandes, R. L., & Ferreira, T. A. E. (2021). Tan-G class of trigonometric distributions and its applications. Cubo, 23(1), 1–20. https://doi.org/10.4067/S0719-06462021000100001
Souzay, L., Júniory, W. R. de O., De Britoz, C. C. R., Chesneaux, C., Ferreiray, T. A. E., & Soaresy, L. G. M. (2019). On the Sin-G class of distributions: Theory, model and application. Journal of Mathematical Modeling, 7(3), 357–379. https://doi.org/10.22124/jmm.2019.13502.1278
Topp, C. W., & Leone, F. C. (1955). A Family of J-Shaped Frequency Functions. Journal of the American Statistical Association, 50(269), 209–219. https://doi.org/10.1080/01621459.1955.10501259
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 UMYU Scientifica
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
&
