Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample
Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
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Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 319; https://doi.org/10.3390/math6120319
Received: 5 November 2018
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Revised: 1 December 2018
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Accepted: 6 December 2018
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Published: 11 December 2018
In this paper, first we consider the maximum likelihood estimators for two unknown parameters, reliability and hazard functions of the generalized Pareto distribution under progressively Type II censored sample. Next, we discuss the asymptotic confidence intervals for two unknown parameters, reliability and hazard functions by using the delta method. Then, based on the bootstrap algorithm, we obtain another two pairs of approximate confidence intervals. Furthermore, by applying the Markov Chain Monte Carlo techniques, we derive the Bayesian estimates of the two unknown parameters, reliability and hazard functions under various balanced loss functions and the corresponding confidence intervals. A simulation study was conducted to compare the performances of the proposed estimators. A real dataset analysis was carried out to illustrate the proposed methods.
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Keywords:
generalized pareto distribution; progressive type ii censored samples; maximum likelihood estimator; delta method; Gibbs and Metropolis-Hasting algorithm; balanced loss function
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MDPI and ACS Style
Hu, X.; Gui, W. Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample. Mathematics 2018, 6, 319. https://doi.org/10.3390/math6120319
AMA Style
Hu X, Gui W. Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample. Mathematics. 2018; 6(12):319. https://doi.org/10.3390/math6120319
Chicago/Turabian StyleHu, Xuehua, and Wenhao Gui. 2018. "Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample" Mathematics 6, no. 12: 319. https://doi.org/10.3390/math6120319
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