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Statistical Inference for the Inverted Scale Family under General Progressive Type-II Censoring

Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
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Symmetry 2020, 12(5), 731; https://doi.org/10.3390/sym12050731
Received: 31 March 2020 / Revised: 15 April 2020 / Accepted: 17 April 2020 / Published: 5 May 2020
Two estimation problems are studied based on the general progressively censored samples, and the distributions from the inverted scale family (ISF) are considered as prospective life distributions. One is the exact interval estimation for the unknown parameter θ , which is achieved by constructing the pivotal quantity. Through Monte Carlo simulations, the average 90 % and 95 % confidence intervals are obtained, and the validity of the above interval estimation is illustrated with a numerical example. The other is the estimation of R = P ( Y < X ) in the case of ISF. The maximum likelihood estimator (MLE) as well as approximate maximum likelihood estimator (AMLE) is obtained, together with the corresponding R-symmetric asymptotic confidence intervals. With Bootstrap methods, we also propose two R-asymmetric confidence intervals, which have a good performance for small samples. Furthermore, assuming the scale parameters follow independent gamma priors, the Bayesian estimator as well as the HPD credible interval of R is thus acquired. Finally, we make an evaluation on the effectiveness of the proposed estimations through Monte Carlo simulations and provide an illustrative example of two real datasets. View Full-Text
Keywords: Monte Carlo simulation; inverted scale family; interval estimation; maximum likelihood estimation; Bayesian estimation; approximate maximum likelihood estimator; Bootstrap method; general progressive Type-II censoring Monte Carlo simulation; inverted scale family; interval estimation; maximum likelihood estimation; Bayesian estimation; approximate maximum likelihood estimator; Bootstrap method; general progressive Type-II censoring
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MDPI and ACS Style

Gao, J.; Bai, K.; Gui, W. Statistical Inference for the Inverted Scale Family under General Progressive Type-II Censoring. Symmetry 2020, 12, 731.

AMA Style

Gao J, Bai K, Gui W. Statistical Inference for the Inverted Scale Family under General Progressive Type-II Censoring. Symmetry. 2020; 12(5):731.

Chicago/Turabian Style

Gao, Jing; Bai, Kehan; Gui, Wenhao. 2020. "Statistical Inference for the Inverted Scale Family under General Progressive Type-II Censoring" Symmetry 12, no. 5: 731.

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