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.

scholarly journals The Gamma Generalized Pareto Distribution with Applications in Survival Analysis

2017 ◽  
Vol 6 (3) ◽  
pp. 141 ◽  
Author(s):  
Thiago A. N. De Andrade ◽  
Luz Milena Zea Fernandez ◽  
Frank Gomes-Silva ◽  
Gauss M. Cordeiro
Keyword(s):  
Monte Carlo Simulation ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Monte Carlo Simulation Study ◽  
Lorenz Curves ◽  
Generalized Pareto ◽  
Mathematical Properties ◽  
Pareto Model

We study a three-parameter model named the gamma generalized Pareto distribution. This distribution extends the generalized Pareto model, which has many applications in areas such as insurance, reliability, finance and many others. We derive some of its characterizations and mathematical properties including explicit expressions for the density and quantile functions, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R\'enyi entropy and order statistics. We discuss the estimation of the model parameters by maximum likelihood. A small Monte Carlo simulation study and two applications to real data are presented. We hope that this distribution may be useful for modeling survival and reliability data.

scholarly journals Inferences for Generalized Pareto Distribution Based on Progressive First-Failure Censoring Scheme

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Rashad M. El-Sagheer ◽  
Taghreed M. Jawa ◽  
Neveen Sayed-Ahmed
Keyword(s):  
Pareto Distribution ◽  
Confidence Region ◽  
Generalized Pareto Distribution ◽  
Simulated Data ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Failure Data ◽  
Generalized Pareto

In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. In addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study.

Inference on P(Y

2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Record Values ◽  
Asymptotic Distributions ◽  
Bayes Estimators ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

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