Pre-test Shrinkage Estimation for Reliability Function of Burr XII Distribution Using Progressive Type II Censored Sample under Precautionary Loss Function (PLF)
DOI:
https://doi.org/10.32792/jeps.v14i3.549Keywords:
Burr XII Distribution, Shrinkage Estimator, Precautionary Loss Function, Reliability Function, Risk Function, Relative Risk, Progressive Type II Censored Sample.Abstract
This article deal with the proposal of suggest and study of the properties of pre-test shrinkage estimators of Reliability Function for the Burr XII distribution using Progressive Type II censored sample. Since some difficulties to derive equations of risk function for proposed shrinkage estimators of reliability function under Precautionary Loss Function (PLF), we to study properties by using Monte-Carlo simulation. The numerical and Monte-Carlo simulations show that the performance of the proposed estimators is better than classical estimators in terms of relative risk.
References
A. E. Gomes, and C. Q. da-Silva, G. M. Cordeiro, "Two extended Burr models: Theory and practice", Communication in Statistics Theory- Methods , vol. 44, pp. 1706-1734, (2015).
A. K. Rao, and H. Pandey, "Bayes estimation under different Loss Function for Exponentiated Weibull distribution", Arya Bhatta Journal of Mathematics and Informatics, vol. 13, no. 1, pp. 19-98, (2021).
A. Karimnezhad, and S. Niazi, A. Parsian, "Bayes and robust Bayes prediction with an application to a rainfall prediction problem". Journal of the Korean Statistical Society, vol. 43,no. 2, pp. 275-291, (2014).
E.K., Al-Hussaini, and A.H., Abdel-Hamid, A.F, Hashem, "One-sample Bayesian prediction intervals based on progressively type-II censored data from the half logistic distribution under progressive stress model", Metrika vol. 78, no. 7 pp. 771 – 783, (2015).
G. Prakash, and D. C. Singh, "Shrinkage estimation in exponential type-II censored data under LINEX loss", Journal of the Korean Statistical Society, vol. 37, pp. 53-61, (2008).
I. W. Burr, "Cumulative frequency functions", Annals of Mathematical Statistics, vol. 13, pp. 215-232, (1942).
J. G. Norstrom, "The use of precautionary loss function in risk analysis", IEEE Transactions on Reliability, vol. 45, pp. 400-403,(1996)..
J. R. Thompson," Some shrunken techniques for estimating the Mean", Journal of the American Statistical Association, vol. 63, pp. 113-122, (1968).
M. Naghizadeh Qomi, and L. Barmoodeh, "Shrinkage testimation in exponential distribution based on records under asymmetric squared log error loss", Journal of Statistical Research of Iran, vol. 12, pp. 225-238, (2015).
N. Balakrishnan, and R. Aggarwala, "Progressive censoring: theory, methods, and applications", Springer Science & Business Media(2000).
N.J. Hassan and M.J. Hadad , A.H. Nasar, "Bayesian shrinkage estimator of Burr XII distribution",(2020).
R. Bantan and A.S. Hassan , E. Almetwally , M. Elgarhy F. Jamal , C. Chesneau , M. Elsehetry, "Bayesian analysis in partially accelerated life tests for weighted Lomax distribution", Comput Mater Contin. Vol. 68, no. 3, pp. 2859-2875, (2021).
R.L. Harrison, "Introduction to monte carlo simulation", In AIP conference proceedings American Institute of Physics, vol.1204, no. 1, pp. 17-21, 2010.
R.R. Abu-Awwad, and M.Z. Raqab, I.M. Al-Mudahakha, "Statistical inference based on progressively type-II censored data from Weibull model", Communications in Statistics – Simulation and Computation, vol. 44, no. 10, pp. 2654-2670, (2015).
R.Y. Rubinstein, and D.P. Kroese, "Simulation and the Monte Carlo method". Joho Wiley & sons, (2016)..
S. Gunasekera, "Inference for the Burr XII reliability under progressive censoring with random removals", Math Comput Simul. Vol. 144, pp. 182-195, (2018).
S. Hossain, and H. Howlader, "Shrinkage estimation in lognormal regression model for censored data", Journal of Applied Statistics, (2016).
X. Qin and W. Gui, "Statistical inference of Burr-XII distribution under progressive Type-II censored competing risks data with binomial removals", J Comput Appl Math. Vol. 378, no. 2, pp. 112922, (2020).
Z. Chen, and W. Liu, "Bayesian Statistical Analysis of Lifetime Performance Index of Exponential Product Under Precautionary Loss Function", In IOP Conference Series: Materials Science and Engineering, IOP Publishing vol. 563, no. 4, pp. 042021, (2019).
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