Algorithms for Generating Neutrosophic Gamma Distributed Data
DOI:
https://doi.org/10.13052/jrss0974-8024.1822Keywords:
Gamma distribution, random variate, indeterminacy, simulation, analysisAbstract
The gamma distribution is well-known for its wide range of applications across various fields. Traditional gamma distributions and their associated algorithms have been used to model imprecise data; however, they face limitations in addressing uncertainty and indeterminacy. To overcome these challenges, this study introduces the neutrosophic gamma distribution, an extension of the classical gamma distribution that incorporates neutrosophic random variables to better handle imprecision and indeterminacy. Basic properties of the neutrosophic gamma distribution are presented, along with algorithms designed to generate data under different levels of indeterminacy. Simulation results reveal that as the degree of indeterminacy increases, the corresponding random variates tend to exhibit an upward trend. Comparative analysis with classical statistics highlights the significant effect of indeterminacy on data generation. Overall, the study demonstrates that the degree of indeterminacy plays a crucial role in shaping the behavior of data derived from the gamma distribution.
Downloads
References
Eric, U., O.M.O. Olusola, and F.C. Eze, A Study of Properties and Applications of Gamma Distribution. Statistics, 2020. 4(2): p. 52–65.
Iriarte, Y.A., et al., A Gamma-Type distribution with applications. Symmetry, 2020. 12(5): p. 870.
Brown, P.J. and J.E. Griffin, Inference with normal-gamma prior distributions in regression problems. 2010. 5 (1): p. 171–188.
Maaref, A. and R. Annavajjala, The gamma variate with random shape parameter and some applications. IEEE communications letters, 2010. 14(12): p. 1146–1148.
Pati, P.S. and P. Krishnan, Modelling of OFDM based RoFSO system for 5G applications over varying weather conditions: A case study. Optik, 2019. 184: p. 313–323.
Huber, F., G. Koop, and L. Onorante, Inducing sparsity and shrinkage in time-varying parameter models. Journal of Business & Economic Statistics, 2021. 39(3): p. 669–683.
Plubin, B. and P. Siripanich, An alternative goodness-of-fit test for a gamma distribution based on the independence property. Chiang Mai J Sci, 2017. 44(3): p. 1180–1190.
Gill, D.J., The Generation of Pseudo Random Numbers from the Gamma Distribution, 1963, Ohio State University.
Atkinson, A. and M. Pearce, The computer generation of beta, gamma and normal random variables. Journal of the Royal Statistical Society: Series A (General), 1976. 139(4): p. 431–448.
Marsaglia, G. and W.W. Tsang, A simple method for generating gamma variables. ACM Transactions on Mathematical Software (TOMS), 2000. 26(3): p. 363–372.
Robertson, I. and L. Walls, Random number generators for the normal and gamma distributions using the ratio of uniforms method, 1980, CM-P00068658.
Tanizaki, H., A simple gamma random number generator for arbitrary shape parameters. Economics Bulletin, 2008. 3(7): p. 1–10.
Apolloni, B. and S. Bassis, Algorithmic inference of two-parameter gamma distribution. Communications in Statistics-Simulation and Computation, 2009. 38(9): p. 1950–1968.
Xi, B., K.M. Tan, and C. Liu, Logarithmic transformation-based gamma random number generators. Journal of Statistical Software, 2013. 55: p. 1–17.
Lawnik, M., Generation of pseudo-random numbers with the use of inverse chaotic transformation. Open Mathematics, 2018. 16(1): p. 16–22.
Luengo, E.A., Gamma Pseudo Random Number Generators. ACM Computing Surveys, 2022. 55(4): p. 1–33.
Smarandache, F., Introduction to neutrosophic statistics: Infinite Study. Romania-Educational Publisher, Columbus, OH, USA, 2014.
Chen, J., J. Ye, and S. Du, Scale effect and anisotropy analyzed for neutrosophic numbers of rock joint roughness coefficient based on neutrosophic statistics. Symmetry, 2017. 9(10): p. 208.
Chen, J., et al., Expressions of rock joint roughness coefficient using neutrosophic interval statistical numbers. Symmetry, 2017. 9(7): p. 123.
Smarandache, F., 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, 2022. 19(1): p. 148–165.
Granados, C., A.K. Das, and D.A.S. Birojit, Some continuous neutrosophic distributions with neutrosophic parameters based on neutrosophic random variables. Advances in the Theory of Nonlinear Analysis and its Application, 2022. 6(3): p. 380–389.
Aslam, M., Truncated variable algorithm using DUS-neutrosophic Weibull distribution. Complex & Intelligent Systems, 2023. 9(3): p. 3107–3114.
Aslam, M., Simulating imprecise data: sine–cosine and convolution methods with neutrosophic normal distribution. Journal of Big Data, 2023. 10(1): p. 143.
Guo, Y. and A. Sengur, NCM: Neutrosophic c-means clustering algorithm. Pattern Recognition, 2015. 48(8): p. 2710–2724.
Garg, H., Algorithms for single-valued neutrosophic decision making based on TOPSIS and clustering methods with new distance measure. Aims Mathematics, 2020. 5(3): p. 2671–2693.
Khan, Z., et al., On statistical development of neutrosophic gamma distribution with applications to complex data analysis. Complexity, 2021. 2021(1): p. 3701236.
Granados, C., A.K. Das, and B. Das, Some continuous neutrosophic distributions with neutrosophic parameters based on neutrosophic random variables. Advances in the Theory of Nonlinear Analysis and its Application, 2022. 6(3): p. 380–389.
Aslam, M. and F.S. Alamri, Algorithm for generating neutrosophic data using accept-reject method. Journal of Big Data, 2023. 10(1): p. 175.
Jdid, M., R. Alhabib, and A. Salama, The basics of neutrosophic simulation for converting random numbers associated with a uniform probability distribution into random variables follow an exponential distribution. Neutrosophic Sets and Systems, 2023. 53(1): p. 22.
Jdid, M., F. Smarandache, and K. Al Shaqsi, Generating Neutrosophic Random Variables Based Gamma Distribution. Plithogenic Logic and Computation, 2024. 1: p. 16–20.
Aslam, M., The neutrosophic negative binomial distribution: algorithms and practical application: accepted-August 2024. REVSTAT-Statistical Journal, 2024. https://revstat.ine.pt/index.php/REVSTAT/article/view/781.
Jdid, M. and F. Smarandache, Generating Neutrosophic Random Variables Following the Poisson Distribution Using the Composition Method (The Mixed Method of Inverse Transformation Method and Rejection Method). Neutrosohic Sets and Systems, 2024. 64: p. 132–140.
Aslam, M., Developing Novel Algorithms for Generating Inexact Data through Triangle Distribution. IEEE Transactions on Big Data, 2024. DOI: nolinkurl10.1109/TBDATA.2024.3460529.
Alamri, F.S. and M. Aslam, Data generation and application using the neutrosophic Erlang distribution. Journal of Big Data, 2025. 12(1): p. 48.
Thomopoulos, N.T., Essentials of Monte Carlo simulation: Statistical methods for building simulation models. 2014: Springer.
Ahrens, J.H. and U. Dieter, Computer methods for sampling from gamma, beta, poisson and bionomial distributions. Computing, 1974. 12(3): p. 223–246.
Cheng, R., The generation of gamma variables with non-integral shape parameter. Journal of the Royal Statistical Society Series C: Applied Statistics, 1977. 26(1): p. 71–75.
Lu, W. and T.-R. Tsai, Interval censored sampling plans for the gamma lifetime model. European Journal of Operational Research, 2009. 192(1): p. 116–124.
Gupta, S.S. and S.S. Gupta, Gamma distribution in acceptance sampling based on life tests. Journal of the American Statistical Association, 1961. 56(296): p. 942–970.
Lee, A.H., et al., Designing acceptance sampling plans based on the lifetime performance index under gamma distribution. The International Journal of Advanced Manufacturing Technology, 2021. 115: p. 3409–3422.
