1
Department of Business Administration, College of Sciences and the Human Sciences in Alaflaj Prince Sattam Bin Abdulaziz University, Saudi Arabia
(am.ibrahim@psau.edu.sa)
2
Department of Mathematics, Hazara University Mansehra, Pakistan
(zahidkhan@hu.edu.pk)
3
Mathematics Department, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia; Business Administration Department, Administrative Science College, Thamar University, Thamar, Yemen
(f.alduais@psau.edu.sa)
Abstract :
The logistic distribution is widely used to model various types of applied data. The modified logistic distribution under neutrosophic statistics is introduced in this work. The neutrosophic logistic distribution (NLD) and its engineering applications are mainly emphasized. An appealing characteristic of the suggested NLD is that it is useful to many widely utilized survival assessment metrics, including the reliability function, hazard function, and survival function. Applications of some mathematical and statistical properties of the suggested model are discussed. Numerical investigations on simulated data are used to validate the theoretical findings experimentally. From an application point of view, it is inferred that the proposed distribution fits data with imprecise, hazy, and fuzzy information better than the usual model. In addition, the maximum likelihood (ML) technique for the proposed model is discussed under the neutrosophic inference framework. Eventually, some illustrative examples related to system reliability are provided to clarify further the implementation of the neutrosophic probabilistic model in real-world problems.
Keywords :
Imprecise data; fuzzy statistics; neutrosophic probability; simulation; maximum likelihood estimation; Reliability
References :
[1] Pycke, J. R., A new family of omega-square-type statistics with Bahadur local optimality for the location family of generalized logistic distributions. Stat. Probab. Lett., vol. 170, p. 108999, 2021.
[2] Kumar, C. S. & Manju, L., Gamma Generalized Logistic Distribution: Properties and Applications. J. Stat. Theory Appl., vol. 21, no. 3, pp. 155–174, 2022.
[3] Mestry, D. V., & Bhowmick, A. R., On estimating the parameters of generalized logistic model from census data: Drawback of classical approach and reliable inference using Bayesian framework. Ecol. Inform., vol. 62, p. 101249, 2021.
[4] Rasekhi, M., Saber, M. M., & Yousof, H. M., Bayesian and classical inference of reliability in multicomponent stress-strength under the generalized logistic model. Commun. Stat., vol. 50, no. 21, pp. 5114–5125, 2020.
[5] Nigm, E. M., Records from reversed generalized logistic distribution and associated inference. J. Appl. Math. Comput. 2008 281, vol. 28, no. 1, pp. 249–264, 2008.
[6] Surendran, S. Tota-Maharaj, K., Log logistic distribution to model water demand data. Procedia Eng., vol. 119, no. 1, pp. 798–802, 2015.
[7] Li, G., & Qin, J., Analysis of two-sample truncated data using generalized logistic models. J. Multivar. Anal., vol. 97, no. 3, pp. 675–697, 2006.
[8] Mehdi S. M., & Yousof, H. M., Bayesian and Classical Inference for Generalized Stress-strength Parameter under Generalized Logistic Distribution. Stat. Optim. Inf. Comput., vol. x, pp. 0–12, 2021.
[9] Mathai, A. M., & Provost, S. B., On q-logistic and related models. IEEE Trans. Reliab., vol. 55, no. 2, pp. 237–244, 2006.
[10] Seo, J. I., & Kang, S. B., Notes on the exponentiated half logistic distribution. Appl. Math. Model., vol. 39, no. 21, pp. 6491–6500, 2015.
[11] Sun, R., Liu, M., & Zhao, L., Research on logistics distribution path optimization based on PSO and IoT. Int. J. Wavelets Multiresolution Inf., vol. 17, no. 6, 2019.
[12] Yager, R. R., Decision making with fuzzy probability assessments, IEEE Trans. Fuzzy Syst., vol. 7, no. 4, pp. 462–467, 1999.
[13] Patro, S. K., & Smarandache, F., The neutrosophic statistical distribution, more problems, more solutions. Infinite Study, 2016.
[14] Li, E. L., & Zhong, Y.-M., Random variable with fuzzy probability. Appl. Math. Mech. 2003 244, vol. 24, no. 4, pp. 491–498, 2003.
[15] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst., vol. 1, no. 1, pp. 3–28, 1978.
[16] Yu, G., Measures of uncertainty for a fuzzy probabilistic information system. Int. J. Gen. Syst., vol. 50, no. 5, pp. 580–618, 2021.
[17] Figueroa-Garcia, J. C., Varon-Gaviria, C. A., & Barbosa-Fontecha, J. L., Fuzzy random variable generation using α-cuts. IEEE Trans. Fuzzy Syst., vol. 29, no. 3, pp. 539–548, 2021.
[18] Smarandache, F., A unifying field in logics: neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic probability. American Research Press, Rehoboth, 1999.
[19] Smarandache, F., Neutrosophical statistics. Sitech & Education publishing, 2014.
[20] Khan, Z., Gulistan, M., Chammam, W., Kadry, S., & Nam, Y., A new dispersion control chart for handling the neutrosophic data. IEEE Access, vol. 8, pp. 96006–96015, 2020.
[21] Aslam, M., Analyzing wind power data using analysis of means under neutrosophic statistics. Soft Comput., vol. 25, no. 10, pp. 7087–7093, 2021.
[22] Aslam, M., Arif, O. H., & Sherwani, R. A. K., New diagnosis test under the neutrosophic statistics: An application to diabetic patients. Biomed Res. Int., vol. 2020, 2020.
[23] Haq, M. A. U., Neutrosophic kumaraswamy distribution with engineering application. NSS, vol. 49, no.1, p.17, 2022.
[24] Khan, Z., Gulistan, M., Hashim, R., Yaqoob, N., & Chammam, W., Design of S-control chart for neutrosophic data: An application to manufacturing industry. J. Intell. Fuzzy Syst., vol. 38, no. 4, pp. 4743–4751, 2020.
[25] Khan, Z., Gulistan, M., Kausar, N. & Park, C., Neutrosophic rayleigh model with some basic characteristics and engineering applications. IEEE Access, vol. 9, pp. 71277–71283, 2021.
[26] Aslam, M., Khan, N., & Khan, M., Monitoring the variability in the process using neutrosophic statistical interval method. Symmetry, vol. 10, no. 11, p. 562, 2018.
[27] Duan, W.Q., Khan, Z., Gulistan, M. & Khurshid, A., Neutrosophic exponential distribution: modeling and applications for complex data analysis. Complexity, vol. 2021, pp. 1–8, 2021.
[28] Aslam. M., Analyzing wind power data using analysis of means under neutrosophic statistics. Soft Computing, vol. 25, no.10, p. 7087-7093, 2021.
[29] Zhang, X., Bo, C., Smarandache, F., & Park, C., New operations of totally dependent-neutrosophic sets and totally dependent-neutrosophic soft sets. Symmetry, vol.10, no.6, p. 187, 2018.
[30] Abdelfattah,. A. M., Skew-Type I generalized logistic distribution and its properties. Pak. J. Stat. Oper. Res., vol. 11, no.3, pp. 267-282, 2015.
| Style | # |
|---|---|
| MLA | A. M. Mohamed Ibrahim, Zahid Khan, Fuad S. Al-Duais. "A New Modified Logistic Distribution: Properties and Applications in Uncertainty Data Modeling." International Journal of Neutrosophic Science, Vol. 20, No. 2, 2023 ,PP. 27-39 (Doi : https://doi.org/10.54216/IJNS.200203) |
| APA | A. M. Mohamed Ibrahim, Zahid Khan, Fuad S. Al-Duais. (2023). A New Modified Logistic Distribution: Properties and Applications in Uncertainty Data Modeling. Journal of International Journal of Neutrosophic Science, 20 ( 2 ), 27-39 (Doi : https://doi.org/10.54216/IJNS.200203) |
| Chicago | A. M. Mohamed Ibrahim, Zahid Khan, Fuad S. Al-Duais. "A New Modified Logistic Distribution: Properties and Applications in Uncertainty Data Modeling." Journal of International Journal of Neutrosophic Science, 20 no. 2 (2023): 27-39 (Doi : https://doi.org/10.54216/IJNS.200203) |
| Harvard | A. M. Mohamed Ibrahim, Zahid Khan, Fuad S. Al-Duais. (2023). A New Modified Logistic Distribution: Properties and Applications in Uncertainty Data Modeling. Journal of International Journal of Neutrosophic Science, 20 ( 2 ), 27-39 (Doi : https://doi.org/10.54216/IJNS.200203) |
| Vancouver | A. M. Mohamed Ibrahim, Zahid Khan, Fuad S. Al-Duais. A New Modified Logistic Distribution: Properties and Applications in Uncertainty Data Modeling. Journal of International Journal of Neutrosophic Science, (2023); 20 ( 2 ): 27-39 (Doi : https://doi.org/10.54216/IJNS.200203) |
| IEEE | A. M. Mohamed Ibrahim, Zahid Khan, Fuad S. Al-Duais, A New Modified Logistic Distribution: Properties and Applications in Uncertainty Data Modeling, Journal of International Journal of Neutrosophic Science, Vol. 20 , No. 2 , (2023) : 27-39 (Doi : https://doi.org/10.54216/IJNS.200203) |