1
Department of Business Administration, College of Sciences and the Human Sciences in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
(am.ibrahim@psau.edu.sa)
2
Department of Quantitative Methods, Pannon Egyetem, Veszprem, H-8200, Hungary
(khan.zahid@gtk.uni-pannon.hu)
Abstract :
This paper introduces the concept of the neutrosophic Laplace distribution ( ), a probability distribution derived from the Laplace distribution. The offers a versatile framework for describing various real-world problems. We highlight the neutrosophic extension of the Laplace distribution and explore its applications in different areas. Extensive investigations into the mathematical properties of the distribution are presented, including the derivation of its probability density function, mean, variance, raw moment, skewness, and kurtosis. To estimate the parameters of the , we employ the method of maximum likelihood (ML) estimation within a neutrosophic environment. Furthermore, we conduct a simulation study to assess the effectiveness of the maximum likelihood approach in estimating the parameters of this new distribution. The findings demonstrate the potential of the in modeling and analyzing real-world phenomena. 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 :
Neutrosophic probability; Laplace distribution; maximum likelihood estimation; simulation
References :
[1] Aryal, G. R., Study of Laplace and related probability distributions and their applications, Graduate School Theses and Dissertations, University of South Florida. 2006.
[2] Rosser Jr, J. B., Reconsidering periodicity and fundamental uncertainty, Journal of Post Keynesian Economics, 38(3), 331-354, 2015.
[3] George, D., & George, S., Marshall-Olkin Esscher transformed Laplace distribution and processes, Brazilian Journal of Probability and Statistics, 162-184, 2013.
[4] McGill, W. J., Random fluctuations of response rate, Psychometrika, 27(1), 3-17, 1962.
[5] Nekoukhou, V., & Alamatsaz, M. H., A family of skew-symmetric-Laplace distributions, Statistical papers, 53(3), 685-696, 2012.
[6] Geraci, M., & Borja, M. C., Notebook: The Laplace distribution, 2018.
[7] Hsu, D. A., Long‐tailed distributions for position errors in navigation, Journal of the Royal Statistical Society: Series C (Applied Statistics), 28(1), 62-72, 1979.
[8] Wilson, E. B., First and second laws of error, Journal of the American Statistical Association, 18(143), 841-851, 1923.
[9] Kozubowski, T. J., & Nadarajah, S., Multitude of Laplace distributions, Statistical Papers, 51(1), 127, 2010.
[10] Smarandache, F., Neutrosophic logic: generalization of the Intuitionistic fuzzy logic, Extr. Metal. Nickel Cobalt Platin. Group Metals, 269(50), 49-53, 2016.
[11] Smarandache, F., A unifying field in logics: neutrosophic logic. Neutrosophy, neutrosophic set, neutrosophic probability: neutrsophic logic, 2005.
[12] Khalid, H. E., Smarandache, F., & Essa, A. K., The basic notions for (over, off, under) neutrosophic geometric programming problems, Infinite Study, 2018.
[13] Smarandache, F., Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis, 1998.
[14] Smarandache, F., Introduction to Neutrosophic Statistics, Sitech & Education Publishing, Craiova, 2014, 124 p.
[15] Duan, W. Q., Khan, Z., Gulistan, M., & Khurshid, A., Neutrosophic exponential distribution: Modeling and applications for complex data analysis, Complexity, 2021, 1-8.
[16] Patro, S. K., & Smarandache, F., The neutrosophic statistical distribution, more problems, more solutions, Infinite Study, 2016.
[17] Aslam, M., A variable acceptance sampling plan under neutrosophic statistical interval method, Symmetry, 11(1), 114, 2019.
[18] Schweizer, P., Uncertainty: two probabilities for the three states of neutrosophy, International Journal of Neutrosophic Science, 2(1), 18-26, 2020.
[19] Arif, O. H., & Aslam, M., A new sudden death chart for the Weibull distribution under complexity, Complex & Intelligent Systems, 7, 2093-2101, 2021.
[20] Aslam, M., Analyzing wind power data using analysis of means under neutrosophic statistics, Soft Computing, 25(10), 7087-7093, 2021.
[21] Aslam, M., Arif, O. H., & Sherwani, R. A. K., New diagnosis test under the neutrosophic statistics: an application to diabetic patients, BioMed Research International, 2020.
[22] Chen, J., Ye, J., Du, S., & Yong, R., Expressions of rock joint roughness coefficient using neutrosophic interval statistical numbers, Symmetry, 9(7), 123, 2017.
[23] Smarandache, F., & Savoiu, G., Neutrosophic index numbers: neutrosophic logic applied in the statistical indicators theory, A Publication of Society for Mathematics of Uncertainty, 10, 67, 2015.
[24] Aslam, M., Bantan, R. A., & Khan, N., Design of a new attribute control chart under neutrosophic statistics, International Journal of Fuzzy Systems, 21, 433-440, 2019.
[25] Khan, Z., Gulistan, M., Kadry, S., Chu, Y., & Lane-Krebs, K., On scale parameter monitoring of the Rayleigh distributed data using a new design, IEEE access, 8, 188390-188400, 2020.
[26] Khan, Z., Gulistan, M., Chammam, W., Kadry, S., & Nam, Y., A new dispersion control chart for handling the neutrosophic data, IEEE access, 8, 96006-96015, 2020.
[27] Khan, Z., Gulistan, M., Hashim, R., Yaqoob, N., & Chammam, W., Design of S-control chart for neutrosophic data: An application to manufacturing industry, Journal of Intelligent & Fuzzy Systems, 38(4), 4743-4751, 2020.
[28] Khan, Z., Gulistan, M., Kausar, N., & Park, C., Neutrosophic Rayleigh model with some basic characteristics and engineering applications, IEEE Access, 9, 71277-71283, 2021.
[29] M. Palanikumar,Aiyared Iampan,Said Broumi, MCGDM based on VIKOR and TOPSIS proposes neutrsophic Fermatean fuzzy soft with aggregation operators, International Journal of Neutrosophic Science, Vol. 19 , No. 3 , (2022) : 85-94 (Doi : https://doi.org/10.54216/IJNS.190308)
[30] P. Reena Joice,M. Trinita Pricilla,S. Broumi, Generalized Pre-closed Sets in Fermatean Neutrosophic Hypersoft Topological Spaces, International Journal of Neutrosophic Science, Vol. 20 , No. 3 , (2023) : 82-97 (Doi : https://doi.org/10.54216/IJNS.200308)
[31] Broumi, S., Sundareswaran, R., Shanmugapriya, M., Bakali, A., & Talea, M. Theory and Applications of Fermatean Neutrosophic Graphs. Neutrosophic Sets and Systems, 50, 248-286. 2022.
[32] Nabil M. AbdelAziz,Hassan H. Mohammed,Khalid A. Eldrandaly, An effective Decision making model through Fusion Optimization and risk associated with flash flood hazards: A case study Asyut, Egypt, Fusion: Practice and Applications, Vol. 12 , No. 1 , (2023) : 64-94 (Doi : https://doi.org/10.54216/FPA.120105)
| Style | # |
|---|---|
| MLA | Ahmedia Musa M. Ibrahim, Zahid Khan. "Neutrosophic Laplace Distribution with Properties and Applications in Decision Making." International Journal of Neutrosophic Science, Vol. 23, No. 1, 2024 ,PP. 73-84 (Doi : https://doi.org/10.54216/IJNS.230106) |
| APA | Ahmedia Musa M. Ibrahim, Zahid Khan. (2024). Neutrosophic Laplace Distribution with Properties and Applications in Decision Making. Journal of International Journal of Neutrosophic Science, 23 ( 1 ), 73-84 (Doi : https://doi.org/10.54216/IJNS.230106) |
| Chicago | Ahmedia Musa M. Ibrahim, Zahid Khan. "Neutrosophic Laplace Distribution with Properties and Applications in Decision Making." Journal of International Journal of Neutrosophic Science, 23 no. 1 (2024): 73-84 (Doi : https://doi.org/10.54216/IJNS.230106) |
| Harvard | Ahmedia Musa M. Ibrahim, Zahid Khan. (2024). Neutrosophic Laplace Distribution with Properties and Applications in Decision Making. Journal of International Journal of Neutrosophic Science, 23 ( 1 ), 73-84 (Doi : https://doi.org/10.54216/IJNS.230106) |
| Vancouver | Ahmedia Musa M. Ibrahim, Zahid Khan. Neutrosophic Laplace Distribution with Properties and Applications in Decision Making. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 1 ): 73-84 (Doi : https://doi.org/10.54216/IJNS.230106) |
| IEEE | Ahmedia Musa M. Ibrahim, Zahid Khan, Neutrosophic Laplace Distribution with Properties and Applications in Decision Making, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 1 , (2024) : 73-84 (Doi : https://doi.org/10.54216/IJNS.230106) |