Jaafer Hmood Eidi This email address is being protected from spambots. You need JavaScript enabled to view it.1 and Makki A. Mohammed Salih 1
1Department of Mathematics, College of Education, Almustansiriyah University-Baghdad-Iraq
Received: October 5, 2021 Accepted: December 28, 2021 Publication Date: February 2, 2022
Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.
Some estimators were used to estimate parameters and reliability function of the Transmuted Rayleigh (TR) distribution, namely, moments (MOM) and modified moments(MM), least squares (LS), weighted least squares (WLS), new white (NW), and the maximum likelihood Estimation (MLE), where the simulation method was used to generate the required data, where a sample size (n = 10, 50 and 100), repeated sample (N = 1000) and the real value of the parameters for four experiments. The obtained results were compared by mean square error. In general, the results showed that both the of MLE and MOM are the best in estimating scale parameter, but in estimating the transmuted parameter, MLE is the best, and in estimating reliability function, the NW is the better than the rest of the methods.
Keywords: Transmuted Rayleigh distribution, Estimation methods, Simulation, Mean square error
REFERENCES
[1] E. Vllah and M. Shahazad, (2016) “Transmutation of the two parameters Rayleigh distribution" International Journal of Advanced Statistics and Probability 4(2): 95–101.
[2] S. Dey, T. Dey, and D. Kundu, (2014) “Two-parameter Rayleigh distribution: different methods of estimation" American Journal of Mathematical and Management Sciences 33(1): 55–74.
[3] W. T. Shaw and I. R. Buckley, (2009) “The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map" arXiv preprint arXiv:0901.0434:
[4] M. A. M. Salih and J. H. Eidi. “Using Simulation to Estimate Reliability Function for Transmuted Kumaraswamy Distribution”. In: IOP Conference Series: Materials Science and Engineering. 928. 4. IOP Publishing. 2020, 042046.
[5] Y. Wu and P. Yang, (2020) “Optimal estimation of Gaussian mixtures via denoised method of moments" The Annals of Statistics 48(4): 1981–2007.
[6] M. A. M. Salih and J. H. Eidi, (2022) “New White Method of Parameters and Reliability Estimation for Transmuted Power Function Distribution" Baghdad Science Journal 19(1): 0077–0077.
[7] M. A. M. Salih and J. H. Eidi, (2022) “New White Method of Parameters and Reliability Estimation for Transmuted Power Function Distribution" Baghdad Science Journal 19(1): 0077–0077.
[8] H.-L. Lu and S.-H. Tao, (2007) “The estimation of Pareto distribution by a weighted least square method" Quality & Quantity 41(6): 913–926.
[9] M. A. M. Saleh, (2006) “Simulation of the methods of the scale parameter and the reliability function Estimation for two parameters Weibull distribution" Doctor of Philosophy in Mathematics, College of Education at Al-Mustansiriyah University:
[10] F.-J. Liu, H.-H. Ko, S.-S. Kuo, Y.-H. Liang, T.-P. Chang, et al., (2014) “Study on wind characteristics using bimodal mixture Weibull distribution for three wind sites in Taiwan" Journal of Applied Science and Engineering 17(3): 283–292.
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