1
Department of Statistics and Informatics, University of Mosul, Mosul, Iraq
(alanadham0@gmail.com)
2
Department of Statistics and Informatics, University of Mosul, Mosul, Iraq
(zakariya.algamal@uomosul.edu.iq)
Abstract :
A relatively recent area of research known as neutrosophic statistics deals with data that are ambiguous, indeterminate, and inconsistent. By embracing the idea of neutrosophy, which denotes the existence of three components in a statement: truth, falsity, and indeterminacy, it broadens the application of classical statistics. One of the significant offshoots of statistics is life-time data analysis. Traditional statistical methods only account for variation within the data and calculate lifetime observations as accurate numbers. Actually, there are two different kinds of uncertainty in data: fluctuation between observations and fuzziness. As a result, analysis techniques that solely employ precise lifetime data and ignore fuzziness use incomplete information and produce false results. This paper sought to generalize hazard rates, survival functions, and parameter estimates for fuzzy Gompertz Distribution. Simulation studies are implemented to examine the performance of the fuzzy Gompertz Distribution. The results show that the fuzzy Gompertz Distribution has better flexibility in handling over the standard Gompertz Distribution.
Keywords :
Gompertz Distribution; fuzzy numbers , neutrosophic statistics; survival analysis; hazard function.
References :
[1] M. Cockeran, S. G. Meintanis, and J. S. Allison, "Goodness-of-fit tests in the Cox proportional hazards model," Communications in Statistics - Simulation and Computation, pp. 1-12, 2019.
[2] T. Emura, Y. H. Chen, and H. Y. Chen, "Survival prediction based on compound covariate under Cox proportional hazard models," PLoS One, vol. 7, p. e47627, 2012.
[3] A. Bouchet, M. Sesma-Sara, G. Ochoa, H. Bustince, S. Montes, and I. Díaz, "Measures of embedding for interval-valued fuzzy sets," Fuzzy Sets and Systems, vol. 467, p. 108505, 2023/09/15/ 2023.
[4] T. Tan and T. Zhao, "A data-driven fuzzy system for the automatic determination of fuzzy set type based on fuzziness," Information Sciences, vol. 642, p. 119173, 2023/09/01/ 2023.
[5] A. A. Ewees, L. Abualigah, D. Yousri, Z. Y. Algamal, M. A. A. Al-qaness, R. A. Ibrahim, et al., "Improved Slime Mould Algorithm based on Firefly Algorithm for feature selection: A case study on QSAR model," Engineering with Computers, vol. 38, pp. 2407-2421, 2022/08/01 2022.
[6] Z. Y. Algamal, M. H. Lee, and A. M. J. J. o. C. Al‐Fakih, "High‐dimensional quantitative structure–activity relationship modeling of influenza neuraminidase a/PR/8/34 (H1N1) inhibitors based on a two‐stage adaptive penalized rank regression," vol. 30, pp. 50-57, 2016.
[7] A. F. Lukman, Z. Y. Algamal, B. G. Kibria, K. J. C. Ayinde, C. Practice, and Experience, "The KL estimator for the inverse Gaussian regression model," vol. 33, p. e6222, 2021.
[8] Z. J. E. J. o. A. S. A. Algamal, "An efficient gene selection method for high-dimensional microarray data based on sparse logistic regression," vol. 10, pp. 242-256, 2017.
[9] F. Smarandache, "Neutrosophic Statistics is an extension of Interval Statistics, while Plithogenic Statistics is the most general form of statistics (second version)," International Journal of Neutrosophic Science, vol. 19, pp. 148-165, 2022.
[10] Z. Khan, A. Amin, S. A. Khan, M. J. N. S. Gulistan, and Systems, "Statistical development of the neutrosophic Lognormal model with application to environmental data," vol. 47, p. 1, 2021.
[11] F. Smarandache, Introduction to neutrosophic statistics: Infinite Study, 2014.
[12] M. J. N. S. S. Ahsan-ul-Haq, "Neutrosophic Kumaraswamy distribution with engineering application," vol. 49, pp. 269-276, 2022.
[13] W.-Q. Duan, Z. Khan, M. Gulistan, A. Khurshid, and Z. Stevic, "Neutrosophic Exponential Distribution: Modeling and Applications for Complex Data Analysis," Complexity, vol. 2021, pp. 1-8, 2021.
[14] C. J. H. J. o. M. Granados and Statistics, "Some discrete neutrosophic distributions with neutrosophic parameters based on neutrosophic random variables," vol. 51, pp. 1442-1457, 2022.
[15] Z. Khan, M. M. A. Almazah, O. Hamood Odhah, H. M. Alshanbari, and T. Mehmood, "Generalized Pareto Model: Properties and Applications in Neutrosophic Data Modeling," Mathematical Problems in Engineering, vol. 2022, pp. 1-11, 2022.
[16] G. S. Rao, "Neutrosophic Log-Logistic Distribution Model in Complex Alloy Metal Melting Point Applications," International Journal of Computational Intelligence Systems, vol. 16, 2023.
[17] F. Shah, M. Aslam, Z. Khan, M. M. A. Almazah, F. S. Alduais, and M. Gulzar, "On Neutrosophic Extension of the Maxwell Model: Properties and Applications," Journal of Function Spaces, vol. 2022, pp. 1-9, 2022.
[18] A. El-Gohary, A. Alshamrani, and A. N. Al-Otaibi, "The generalized Gompertz distribution," Applied Mathematical Modelling, vol. 37, pp. 13-24, 2013/01/01/ 2013.
[19] K. Lee and J.-I. Seo, "Different Approaches to Estimation of the Gompertz Distribution under the Progressive Type-II Censoring Scheme," Journal of Probability and Statistics, vol. 2020, pp. 1-7, 2020.
[20] M. A. Khaleel, N. H. Al-Noor, M. K. J. P. o. E. Abdal-Hameed, and N. Sciences, "Marshall Olkin exponential Gompertz distribution: Properties and applications," vol. 8, pp. 298-312, 2020.
[21] L. A. J. I. Zadeh and control, "Fuzzy sets," vol. 8, pp. 338-353, 1965.
[22] T. Pathinathan, K. J. A. o. P. Ponnivalavan, and A. Mathematics, "Reverse order triangular, trapezoidal and pentagonal fuzzy numbers," vol. 9, pp. 107-117, 2015.
[23] I. Alkanani, F. A. J. M. T. Adnan, and Modeling, "Ranking function methods for solving fuzzy linear programming problems," vol. 4, pp. 65-72, 2014.
| Style | # |
|---|---|
| MLA | Alan Adham Bibani, Zakariya Yahya Algamal. "Survival Function Estimation for Fuzzy Gompertz Distribution with neutrosophic data." International Journal of Neutrosophic Science, Vol. 21, No. 3, 2023 ,PP. 137-142 (Doi : https://doi.org/10.54216/IJNS.210313) |
| APA | Alan Adham Bibani, Zakariya Yahya Algamal. (2023). Survival Function Estimation for Fuzzy Gompertz Distribution with neutrosophic data. Journal of International Journal of Neutrosophic Science, 21 ( 3 ), 137-142 (Doi : https://doi.org/10.54216/IJNS.210313) |
| Chicago | Alan Adham Bibani, Zakariya Yahya Algamal. "Survival Function Estimation for Fuzzy Gompertz Distribution with neutrosophic data." Journal of International Journal of Neutrosophic Science, 21 no. 3 (2023): 137-142 (Doi : https://doi.org/10.54216/IJNS.210313) |
| Harvard | Alan Adham Bibani, Zakariya Yahya Algamal. (2023). Survival Function Estimation for Fuzzy Gompertz Distribution with neutrosophic data. Journal of International Journal of Neutrosophic Science, 21 ( 3 ), 137-142 (Doi : https://doi.org/10.54216/IJNS.210313) |
| Vancouver | Alan Adham Bibani, Zakariya Yahya Algamal. Survival Function Estimation for Fuzzy Gompertz Distribution with neutrosophic data. Journal of International Journal of Neutrosophic Science, (2023); 21 ( 3 ): 137-142 (Doi : https://doi.org/10.54216/IJNS.210313) |
| IEEE | Alan Adham Bibani, Zakariya Yahya Algamal, Survival Function Estimation for Fuzzy Gompertz Distribution with neutrosophic data, Journal of International Journal of Neutrosophic Science, Vol. 21 , No. 3 , (2023) : 137-142 (Doi : https://doi.org/10.54216/IJNS.210313) |