Generalized Z.T. Gao Method for Estimating Three Parameters of Weibull Distribution

Volume 8, Issue 2, April 2023     |     PP. 49-62      |     PDF (1333 K)    |     Pub. Date: April 5, 2023
DOI: 10.54647/computer520345    103 Downloads     160165 Views  

Author(s)

Jiajin Xu, L&Z international leasing Co. Ltd, Canton 510620, China

Abstract
In the process of fatigue research, it is found that most of the fatigue life data of structures conform to Weibull distribution rather than Gaussian distribution, and Weibull distribution is in a sense more general distribution than Gaussian distribution. But the biggest obstacle to the application of Weibull distribution is the complexity of Weibull distribution, especially the estimation of its three parameters is difficult. This is because the correlation coefficient estimation, MLE and other methods proposed by people have a common characteristic that the mathematical derivation is complicated and the calculation is complex. Based on the estimation of the correlation coefficients, author proposed Z.T. Gao method which can avoid these difficulties and can easily estimate the three parameters of Weibull distribution. Further study found that the idea of Z.T. Gao method can be used to avoid the difficulty of MLE, author call it generalized Z.T. Gao method can also conveniently get more ideal results.

Keywords
Three Parameter Weibull Distribution, Correlation Coefficient Estimation, Z.T. Gao (Gao Zhentong) Method, Maximum Likelihood Estimation(MLE), Generalized Z.T. Gao(G- Z.T. Gao) Method

Cite this paper
Jiajin Xu, Generalized Z.T. Gao Method for Estimating Three Parameters of Weibull Distribution , SCIREA Journal of Computer. Volume 8, Issue 2, April 2023 | PP. 49-62. 10.54647/computer520345

References

[ 1 ] Weibull WALODDI, A statistical distribution function of wide applicability[J]. Journal of Applied Mechanic Reliab.,195l，28(4)：613～617．,
[ 2 ] Hallinan A J, A review of the Weibull distribution[J].Journal of Quality Technology，1993，25(2)：85—93．,
[ 3 ] Xu Jiajin, Gao Zhentong Method in Intelligence of Statistics in Fatigue [J], Journal of Beijing University of Aeronautics and Astronautics, 2021,47(10),Doi: 10.13700/j.bh. 1001-5965.2020.0373(in Chinese),
[ 4 ] Fu H M, GAO Z T, An optimization method of correlation coefficient for determining A three-parameters Weibull distribution[J]. Acta Aeronautica et Astronautica Sinica, 1990,11(7):A323-327(in Chinese).,
[ 5 ] Zhao B F, Wu S J, Parameter estimation method for 3-parameter Weibull distribution[J]. Metal Heat Treatment, 2007, 32:443-446(in Chinese).,
[ 6 ] Fan Yang, Hu Ren, and Zhili Hu, Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy[J].Mathematical Problems in Engineering, Volume 2019, Article ID 6281781, 8 pages, https://doi.org/10.1155/2019/6281781,
[ 7 ] Yan X.D.，Ma X.，Zheng R.Y.，WU L, Comparison of the Parameters Estimation Methods for 3 Parameter Weibull Distribution[J]. Journal of Ningbo University, 2005,9,V.18(3) (in Chinese).,
[ 8 ] Hu E.P., Lou X.B., Liu G.Q, Estimation Methods for 3 Parameter Weibull Distribution, Journal of Shenyang Institute of Technology, 2000,9, V.19(3) (in Chinese).,
[ 9 ] Mahdi Teimouri, d Arjun K. Gupta, On the Three-Parameter Weibull Distribution Shape Parameter Estimation[J]. Journal of Data Science 11(2013), 403-414,
[ 10 ] Shi J.Z., YangＸ.Z., ChenＸ.C, Comparison study on the Parameters Estimation Methods for 3 Parameter Weibull Distribution[J]. Journal of Henan Agricultural University,2009, 8,V.43(4) (in Chinese).,
[ 11 ] Gao Z.T., Xu J.J, Intelligent Fatigue Statistics [M].Beijing: Beihang publishing house, 2022:18,23,128(in Chinese),
[ 12 ] Gao Z T, Fatigue applied statistics [M].Beijing: National Defense Industry Press,1986: 83,136,231,253 (in Chinese).,
[ 13 ] Trivedi K.S, Probability and Statistics with Reliability, Queuing, and Computer Science Applications[M].2nd,Bejing: Electronic Industry Press,2015:601-602(in Chinese).,
[ 14 ] Xu J.J.,GAO Z T, Further research on fatigue statistics intelligence[J]. Acta Aeronautica et Astronautica Sinica, 2022: 43(8):225138 (in Chinese). doi:10 7527/S1000-6893.2021.25138,
[ 15 ] Jiajin Xu. Digital Experiment for Estimating Three Parameters and Their Confidence Intervals of Weibull Distribution[J]. International Journal of Science, Technology and Society. Vol. 10, No. 2, 2022, pp. 72-81. doi: 10.11648/j.ijsts.20221002.16 ,