Volume 4 • Issue 2 • PP: 08-23 • 2023
Random Numbers Generation and Goodness-of-Fit Testing for Literal Neutrosophic Numbers
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This paper presents an algorithm for generating random numbers that follow literal neutrosophic distributions using algebraic isomorphisms. The algorithm was applied to three distributions: literal neutrosophic uniform distribution, literal neutrosophic exponential distribution, and literal neutrosophic normal distribution. We also proposed a development of the Kolmogorov-Smirnov test to analyze goodness-of-fit for literal neutrosophic data. To evaluate the effectiveness of the proposed method, a simulation study was conducted, and the power results showed that increasing the sample size improved the test power. Our research contributes to the development of statistical methods for analyzing literal neutrosophic data, which has applications in a wide range of fields.
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References
|
[1] |
S. M. Ross, Introduction to probability models, 10 ed., United States: Academic Press, 2019. |
|
[2] |
L. Devroye, Non-Uniform Random Variate Generation, New York: Springer, 1986. |
|
[3] |
G. S. Fishman, Monte Carlo: concepts, algorithms, and applications, New York: Springer, 1996. |
|
[4] |
D. E. Knuth, The Art of Computer Programming, vol. 2, United States: Addison-Wesley, 1998. |
|
[5] |
P. L'Ecuyer and R. Simard, "TestU01: A C library for empirical testing of random number generators," ACM Transactions on Mathematical Software, vol. 33, no. 4, pp. 1-40, 2007. |
|
[6] |
M. Aslam, "Introducing Kolmogorov−Smirnov Tests under Uncertainty: An Application to Radioactive Data," ACS Omega, vol. 5, pp. 914-917, 2020. |
|
[7] |
M. Aslam, "A new goodness of fit test in the presence of uncertain parameters," Complex & Intelligent Systems, vol. 7, pp. 359-365, 2021. |
|
[8] |
M. Ahsan-ul-Haq, "A new Cramèr–von Mises Goodness-of-fit test under Uncertainty," Neutrosophic Sets and Systems, vol. 49, pp. 262-268, 2022. |
|
[9] |
M. Aslam, "Chi-square test under indeterminacy: an application using pulse count data," BMC Med Res Methodology, vol. 21, no. 1, 2021. |
|
[10] |
M. Jdid, R. Alhabib and A. A. Salama, "Fundamentals of Neutrosophical Simulation for Generating Fundamentals of Neutrosophical Simulation for Generating Random Numbers Associated with Uniform Probability Random Numbers Associated with Uniform Probability Distribution," Neutrosophic Sets and Systems, vol. 49, pp. 92-102, 2022. |
|
[11] |
M. B. Zeina and M. Abobala, "A Novel Approach of Neutrosophic Continuous Probability Distributions using AH-Isometry with Applications in Medicine," in Cognitive Intelligence with Neutrosophic Statistics in Bioinformatics, Elsevier, 2023. |
|
[12] |
M. B. Zeina , O. Zeitouny , F. Masri , F. Kadoura and S. Broumi, "Operations on Single-Valued Trapezoidal Neutrosophic Numbers using (α,β,γ)-Cuts “Maple Package”," International Journal of Neutrosophic Science, vol. 15, no. 2, pp. 113-122, 2021. |
|
[13] |
M. Abobala and M. B. Zeina, "A Study of Neutrosophic Real Analysis by Using the One-Dimensional Geometric AH-Isometry," Galoitica: Journal of Mathematical Structures and Applications, vol. 3, no. 1, pp. 18-24, 2023. |
|
[14]
[15] |
M. B. Zeina and A. Hatip, "Neutrosophic Random Variables," Neutrosophic Sets and Systems, vol. 39, pp. 44-52, 2021. A. Astambli, M. B. Zeina and Y. Karmouta, "On Some Estimation Methods of Neutrosophic Continuous Probability Distributions Using One-Dimensional AH-Isometry," Neutrosophic Sets and Systems, vol. 53, pp. 641-652, 2023. |
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