scholarly journals Characterization of the generalized Pareto distribution by general progressively Type-II right censored order statistics

2017 ◽  
Vol 25 (4) ◽  
pp. 369-374
Author(s):  
Marwa M. Mohie El-Din ◽  
A. Sadek ◽  
Marwa M. Mohie El-Din ◽  
A.M. Sharawy
Keyword(s):  
Order Statistics ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Type Ii ◽  
Generalized Pareto ◽  
Right Censored Order Statistics

Bayesian Survival Analysis for Generalized Pareto Distribution Under Progressively Type II Censored Data

2019 ◽  
Vol 27 (01) ◽  
pp. 2050001
Author(s):  
Shaowei Li ◽  
Wenhao Gui
Keyword(s):  
Pareto Distribution ◽  
Survival Function ◽  
Information Matrix ◽  
Generalized Pareto Distribution ◽  
Delta Method ◽  
Point Estimate ◽  
Type Ii ◽  
Nonparametric Bootstrap ◽  
Monte Carlo Simulation Study ◽  
Generalized Pareto

In this paper, based on the progressively type II censoring data of generalized Pareto distribution, we consider the maximum likelihood estimation and asymptotic interval estimations of survival function and hazard function by using the Fisher information matrix and delta method. Also, we present a nonparametric Bootstrap-p method to generate the bootstrap samples and derive confidence interval estimation. In addition, we propose the Bayes estimator of Adaptive Rejection Metropolis Sampling algorithm to derive the point estimate and credible intervals. Finally, Monte Carlo simulation study is carried out to compare the performances of the three proposed methods based on different data schemes. An illustrative example is presented.

scholarly journals Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 319 ◽  
Author(s):  
Xuehua Hu ◽  
Wenhao Gui
Keyword(s):  
Confidence Intervals ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Delta Method ◽  
Type Ii ◽  
Unknown Parameters ◽  
Hazard Functions ◽  
Generalized Pareto ◽  
Censored Sample ◽  
Type Ii Censored Sample

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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