{"id":5374,"date":"2026-05-03T12:34:44","date_gmt":"2026-05-03T04:34:44","guid":{"rendered":"\/jase\/?post_type=tkuisotope&p=5374"},"modified":"2026-06-26T18:13:19","modified_gmt":"2026-06-26T10:13:19","slug":"parameters-and-reliability-estimation-for-transmuted-rayleigh-distribution","status":"publish","type":"tkuisotope","link":"\/jase\/?tkuisotope=parameters-and-reliability-estimation-for-transmuted-rayleigh-distribution","title":{"rendered":"Parameters and Reliability Estimation for Transmuted Rayleigh Distribution"},"content":{"rendered":"\n
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<\/i> 2022<\/a><\/p>\n<\/div>\n\n\n\n

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<\/i> Volume 25, Issue 6<\/a><\/p>\n<\/div>\n\n\n\n

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Jaafer Hmood Eidi1<\/sup><\/i><\/a> and Makki A. Mohammed Salih1<\/sup><\/i><\/a><\/p>\n\n\n\n

1<\/sup>Department of Mathematics, College of Education, Almustansiriyah University-Baghdad-Iraq<\/p>\n<\/div>\n\n\n\n

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Received:\u00a0October 05, 2021
Accepted:\u00a0December 28, 2021
Publication Date:\u00a0May 03, 2026<\/p>\n<\/div>\n<\/div>\n\n\n\n

\"\u4e0a\u50b3\u5716\u7247\"\n\n\n

Plot the reliability distribution.<\/p>\n<\/div>\n<\/div>\n\n\n\n

<\/i> Copyright <\/strong>The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0)<\/a>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.<\/p>\n\n\n\n

Download Citation:  BibTeX <\/a>| http:\/\/dx.doi.org\/10.6180\/jase.202212_25(6).0007<\/a>  <\/p>\n\n\n\n

Download PDF<\/a><\/p>\n\n\n\n

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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.<\/p>\n\n\n\n

Keywords:\u00a0Transmuted Rayleigh distribution, Estimation methods, Simulation, Mean square error.<\/em><\/p>\n\n\n\n

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  1. [1] E. Vllah and M. Shahazad, (2016) \u201cTransmutation of the two parameters Rayleigh distribution” International Journal of Advanced Statistics and Probability 4(2): 95\u2013101.<\/li>\n
  2. [2] S. Dey, T. Dey, and D. Kundu, (2014) \u201cTwo-parameter Rayleigh distribution: different methods of estimation” American Journal of Mathematical and Management Sciences 33(1): 55\u201374.<\/li>\n
  3. [3] W. T. Shaw and I. R. Buckley, (2009) \u201cThe alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map” arXiv preprint arXiv:0901.0434:<\/li>\n
  4. [4] M. A. M. Salih and J. H. Eidi. \u201cUsing Simulation to Estimate Reliability Function for Transmuted Kumaraswamy Distribution\u201d. In: IOP Conference Series: Materials Science and Engineering. 928. 4. IOP Publishing. 2020, 042046.<\/li>\n
  5. [5] Y. Wu and P. Yang, (2020) \u201cOptimal estimation of Gaussian mixtures via denoised method of moments” The Annals of Statistics 48(4): 1981\u20132007.<\/li>\n
  6. [6] M. A. M. Salih and J. H. Eidi, (2022) \u201cNew White Method of Parameters and Reliability Estimation for Transmuted Power Function Distribution” Baghdad Science Journal 19(1): 0077\u20130077.<\/li>\n
  7. [7] M. A. M. Salih and J. H. Eidi, (2022) \u201cNew White Method of Parameters and Reliability Estimation for Transmuted Power Function Distribution” Baghdad Science Journal 19(1): 0077\u20130077.<\/li>\n
  8. [8] H.-L. Lu and S.-H. Tao, (2007) \u201cThe estimation of Pareto distribution by a weighted least square method” Quality &Quantity 41(6): 913\u2013926.<\/li>\n
  9. [9] M. A. M. Saleh, (2006) \u201cSimulation 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:<\/span><\/li>\n
  10. [<\/span>10] F.-J. Liu, H.-H. Ko, S.-S. Kuo, Y.-H. Liang, T.-P. Chang, et al., (2014) \u201cStudy on wind characteristics using bimodal mixture Weibull distribution for three wind sites in Taiwan” Journal of Applied Science and Engineering 17(3): 283\u2013<\/span>292.<\/li>\n<\/ol>\n<\/div>\n\n\n\n

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