Numerical Methods for Statistical Data Generation
DOI:
https://doi.org/10.29304/jqcsm.2024.16.21550Keywords:
Monte Carlo Simulation, Numerical Methods, Root FindingAbstract
A comprehensive comparison was undertaken between two numerical methods, namely bisection and secant methods, to generate random variable data for distribution. two methodologies were suggested to acquire the initial guesses for secant and interval for the bisection method. The results of 100 cases for the choices of the parameters are shown and a comparison was made according to the number of iterations between the methods that was conducted.
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J. G. P. Barnes, “An Algorithm for Solving Non-Linear Equations Based on the Secant Method,” Comput J, vol. 8, no. 1, pp. 66–72, Apr. 1965, doi: 10.1093/comjnl/8.1.66.
N. Anderson, “On computing eigenvalues of matrices with real eigenvalues by the secant method,” CM-P00069400, 1975.
G. S. Fishman, “A Monte Carlo Sampling Plan for Estimating Network Reliability,” Oper Res, vol. 34, no. 4, pp. 581–594, Aug. 1986, doi: 10.1287/opre.34.4.581.
I. K. Argyros, “On the secant method,” Publ. Math. Debrecen, vol. 43, no. 3–4, pp. 223–238, 1993.
H. D. Simon and S.-H. Teng, “How Good is Recursive Bisection?,” SIAM Journal on Scientific Computing, vol. 18, no. 5, pp. 1436–1445, Sep. 1997, doi: 10.1137/S1064827593255135.
P. Singh, A. Singhal, and S. D. Joshi, “An efficient ML frequency estimation of a sinusoid using the Secant method,” in 2017 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS), Dec. 2017, pp. 1–5. doi: 10.1109/ANTS.2017.8384150.
D. P. Kroese, T. Taimre, and Z. I. Botev, Handbook of monte carlo methods. John Wiley & Sons, 2013.
Intisar Elaiwi Ubaid, “Double Weighted Functions of Some Probability Distributions,” MsC, Mustansiriyah University, Baghdad, 2023.
R. L. Burden and J. D. Faires, “Numerical analysis 8th ed,” Thomson Brooks/Cole, 2005.
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Copyright (c) 2024 Hayder Abdulabbas Hasan
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