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Comparing three estimators of fuzzy reliability for one scale parameter Rayleigh distribution | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 2013-2020 اصل مقاله (1.18 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5338 | ||
| نویسندگان | ||
| Mohammed Kadhim Hawash* 1؛ Suhad Ahmed Ahmed2؛ Dhwyia Salman Hassan3 | ||
| 1Dijlah University College, Baghdad, Iraq. | ||
| 2College of Education Ibn Al Haitham, University of Baghdad, Baghdad, Iraq. | ||
| 3Business information college, University of information Technology and communications, Baghdad, Iraq. | ||
| تاریخ دریافت: 12 اسفند 1399، تاریخ بازنگری: 17 فروردین 1400، تاریخ پذیرش: 12 تیر 1400 | ||
| چکیده | ||
| This paper deals with comparing three different estimators of fuzzy reliability estimator of one scale parameter Rayleigh distribution were first of all the one scale parameter Rayleigh is defined. Afterwards, the cumulative distribution function is derived, as well as the reliability function is also found. The parameters θ is estimated by three different methods, which are maximum likelihood, and moments, as well as the third method of estimation which is called percentile method or Least Square method, where the estimator $(\hat{\vartheta}_{pec})$ obtained from Minimizing the total sum of the square between given C DF, and one non-parametric estimator like $\hat{F}(ti,\theta)=\frac{i}{n+1}$ after the estimator of $(\theta)$, which $(\hat{\theta})$ is obtained. We work on comparing different fuzzy reliability estimators and all the results are explained besides different sets of taking four sample sizes $(n= 20, 40, 60$, and $80)$. | ||
| کلیدواژهها | ||
| Fuzzy Reliability Estimator (FRE)؛ Least Square Estimators (LSE)؛ Maximum Likelihood Estimator (MLE)؛ Moments estimator (MOM)؛ Rayleigh Distribution | ||
| مراجع | ||
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[1] D.S. Hassan, I. Rikan and H. Kadhum, Comparing two estimators of reliability function for three extended Rayleigh distribution, Amer. J. Math. Stat. 7(6) (2017) 237–242. [2] Y.A. Iriarte, N.O. Castillo, H. Bolfarine and H.W. Gomez, Modified slashed-Rayleigh distribution, Comm. Statist. Theo. Methods., 47(13) (2018) 3220–3233. [3] A.F. jameel, R.A. Zaboon, and H.A. Hashim, Solution of fuzzy reliability allocation optimization problems, Appl. Math. Comput. Intel. 4(1) (2015) 325–340. [4] A.S. Malik and S.P. Ahmad, Alpha power Rayleigh distribution and its application to life time data, Int. J. Enhanced Res. Manag. Comput. 6(11) (2017) 212–219. [5] A.C. Mkolesia and M.Y. Shatalov, Exact Solutions for a Two-Parameter Rayleigh Distribution, Global J. Pure Appl. Math. 13(11) (2017) 8039–8051. [6] B. Lahcene, On recent modifications of extended Rayleigh distribution and its applications, J. Fund. Appl. Stat. 11(1–2) (2017) 1–13. [7] M.H. Sabry and E.A. Amin, Fuzzy reliability estimation based on exponential ranked set samples, Int. J. Contemp. Math. Sci. 12(1) (2017) 31–42. [8] H.S. Salinas, Y.A. Iriarte, and H. Bolfarine, Slashed exponentiated Rayleigh distribution, Revista Columbiana Stat. 38(2) 2015 453–466. [9] J.I. Seo, J.W. Jeon and S.B. Kang, Exact interval inference for the two parameter Rayleigh distribution based on the upper record values, J. Prob. Stat. 2016(8246390) (2016) 1–5. [10] H.-J. Zimmermann, Methods and Applications of Fuzzy Mathematical Programming, In: R.R. Yager, L.A. Zadeh (eds) An Introduction to Fuzzy Logic Applications in Intelligent Systems., The Springer International Series in Engineering and Computer Science (Knowledge Representation, Learning and Expert Systems), 1992. | ||
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