Volume 27 , Issue 2 , PP: 95-109, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Anas Abdulbast Abbas 1 *
Doi: https://doi.org/10.54216/IJNS.270209
Uncertainty, imprecision, and incomplete information are commonly found in complex economic and financial systems, and traditional probabilistic models are thus inadequate to accurately model and forecast these systems. In this work, a new extension of the Muth distribution in the neutrosophic environment is presented leading to the neutrosophic Muth distribution (NMD). This new model introduces neutrosophic parameters aiming to quantify vague and uncertain information and provides a flexible and robust approach to modeling right-skewed economic data. Some key characteristics including the density function and cumulative distribution function, moment generating function, and origin moments are obtained in the neutrosophic framework. The study of a model treated under uncertainty is described and an inferential method transforming it into neutrosophic maximum likelihood by interval-valued data is discussed. A real-world financial dataset is considered in order to prove the usefulness of the proposed distribution. The findings emphasize that the proposed distribution has the potential to be a comprehensive, flexible, and potential model for handling uncertainty in economics and finance data.
Neurotrophic logic , Uncertainty modeling , Neutrosophic probability , Estimation , Simulation
[1] M. N. Alshehri et al., "Decision making on determinant and adjoint of a square neutrosophic fuzzy economic model," Contemporary Mathematics, pp. 1127–1137, 2025.
[2] B. Ananth and A. Shah, "Probability distributions," in Financial Engineering for Low-Income Households. SAGE Publications India Pvt Ltd, 2013, pp. 27–39.
[3] J. Das et al., "Economic peaks and value-at-risk analysis: A novel approach using the Laplace distribution for house prices," Mathematical and Computational Applications, vol. 30, no. 1, p. 4, 2025.
[4] L. Chen, X. Wang, and Y. Zhao, "A machine learning framework for integrating uncertainty in economic forecasting models," Expert Systems with Applications, vol. 213, p. 119201, 2023.
[5] C. H. Korkpoe, F. Ahiakpor, and E. N. A. Amarteifio, "Bayesian inference for inflation volatility modeling in Ghana," African Journal of Economic and Management Studies, vol. 16, no. 1, pp. 34–46, 2025.
[6] F. M. Müller, L. T. Spindler, and M. B. Righi, "Comparative analysis of risk measures for optimal hedge ratio determination," Finance Research Letters, vol. 60, p. 106795, 2025.
[7] J. K. Pokharel, G. Aryal, N. Khanal, and C. P. Tsokos, "Probability distributions for modeling stock market returns—An empirical inquiry," International Journal of Financial Studies, vol. 12, no. 2, p. 43, 2024.
[8] P. Stockhammar and L.-E. Öller, "On the probability distribution of economic growth," Journal of Applied Statistics, vol. 38, no. 9, pp. 2023–2041, 2011.
[9] S. Sundararajan, "Introduction to probability and statistics," in Multivariate Analysis and Machine Learning Techniques. Springer, 2025, pp. 81–111.
[10] M. R. Irshad, R. Maya, and S. P. Arun, "Muth distribution and estimation of a parameter using order statistics," Statistica, vol. 81, no. 1, pp. 93–119, 2021.
[10] P. Jodra, M. D. Jimenez-Gamero, and M. V. Alba-Fernandez, "On the Muth distribution," Mathematical Modelling and Analysis, vol. 20, no. 3, pp. 291–310, 2015.
[11] P. Jodra, H. W. Gomez, M. D. Jimenez-Gamero, and M. V. Alba-Fernandez, "The power Muth distribution," Mathematical Modelling and Analysis, vol. 22, no. 2, pp. 186–201, 2017.
[12] M. Á. Gil, M. López-Díaz, and D. A. Ralescu, "Overview on the development of fuzzy random variables," Fuzzy Sets and Systems, vol. 157, no. 19, pp. 2546–2557, 2006.
[13] A. F. Shapiro, "Fuzzy random variables," Insurance: Mathematics and Economics, vol. 44, no. 2, pp. 307–314, 2009.
[14] S. Broumi, M. Talea, A. Bakali, and F. Smarandache, "Interval complex neutrosophic set: Formulation and applications in decision-making," International Journal of Fuzzy Systems, vol. 23, no. 3, pp. 644–671, 2021.
[15] F. Smarandache, "A unifying field in Logics: Neutrosophic Logic," Philosophy, American Research Press, 1999.
[16] F. Smarandache and S. Pramavik, "New trends in neutrosophic theory and its applications," Pons Edition, Brussels, Belgium, EU, 2016.
[17] D. Pamucar, D. Bozanic, and I. Ljubojevic, "Multi-criteria decision-making model for evaluating safety of road sections," Journal of Intelligent and Fuzzy Systems, vol. 38, no. 4, pp. 5013–5030, 2020.
[18] P. Singh, S. S. Borah, and B. Dey, "A novel high-order fuzzy time series forecasting method based on probabilistic fuzzy sets and particle swarm optimization," Engineering Applications of Artificial Intelligence, vol. 115, p. 105294, 2022.
[19] S. Nadarajah and H. Zhang, "A new heavy-tailed distribution for modeling financial returns," Journal of Computational and Applied Mathematics, vol. 394, p. 113562, 2021.
[20] A. Alaita and M. Aslam, "Analysis of covariance under neutrosophic statistics," Journal of Statistical Computation and Simulation, vol. 93, no. 3, pp. 397–415, 2023.
[21] Z. Khan and K. L. Krebs, "Enhancing neutrosophic data analysis: A review of neutrosophic measures and applications with Neutrostat," Neutrosophic Sets and Systems, vol. 78, pp. 181–190, 2025.
