scholarly journals On Truncated Zeghdoudi Distribution : Posterior Analysis under Different Loss Functions for Type II Censored Data

2021 ◽  
pp. 497-508
Author(s):  
Hamida Talhi ◽  
Hiba Aiachi
Keyword(s):  
Censored Data ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Loss Functions ◽  
Model Parameters ◽  
Type Ii ◽  
Bayes Estimators ◽  
Quadratic Entropy ◽  
Type Ii Censored Data ◽  
Bayesian Estimators

We perform a Bayesian analysis of the upper trunacated Zeghdoudi distribution based on type II censored data. Using various loss functions including the generalised quadratic, entropy and Linex functions, we obtain Bayes estimators and the corresponding posterior risks. As tractable analytical forms of these estimators is out of reach, we propose the use of simulations based on Markov chain Monte-carlo methods to study their performance. Given nitial values of model parameters, we also obtain maximum likelihood estimators. Using Pitmanw closeness criterion and integrated mean square error we  compare their performance with those of the Bayesian estimators. Finally, we illustrate our approach through an example using a set of real data.

scholarly journals E-Bayesian Prediction for the Burr XII Model Based on Type-II Censored Data with Two Samples

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hassan M. Okasha ◽  
Chuanmei Wang ◽  
Jianhua Wang
Keyword(s):  
Censored Data ◽  
Real Data ◽  
Bayesian Prediction ◽  
Loss Functions ◽  
Type Ii ◽  
Interval Prediction ◽  
Two Samples ◽  
Type Ii Censored Data ◽  
Lifetime Studies ◽  
Predictive Functions

Type-II censored data is an important scheme of data in lifetime studies. The purpose of this paper is to obtain E-Bayesian predictive functions which are based on observed order statistics with two samples from two parameter Burr XII model. Predictive functions are developed to derive both point prediction and interval prediction based on type-II censored data, where the median Bayesian estimation is a novel formulation to get Bayesian sample prediction, as the integral for calculating the Bayesian prediction directly does not exist. All kinds of predictions are obtained with symmetric and asymmetric loss functions. Two sample techniques are considered, and gamma conjugate prior density is assumed. Illustrative examples are provided for all the scenarios considered in this article. Both illustrative examples with real data and the Monte Carlo simulation are carried out to show the new method is acceptable. The results show that Bayesian and E-Bayesian predictions with the two kinds of loss functions have little difference for the point prediction, and E-Bayesian confidence interval (CI) with the two kinds of loss functions are almost similar and they are more accurate for the interval prediction.

scholarly journals Bayes Estimation of a Two-Parameter Geometric Distribution under Multiply Type II Censoring

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
J. B. Shah ◽  
M. N. Patel
Keyword(s):  
Geometric Distribution ◽  
Correct Choice ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Type Ii ◽  
Expected Loss ◽  
Bayes Estimators ◽  
Linex Loss ◽  
Type Ii Censored Data ◽  
Two Parameter

We derive Bayes estimators of reliability and the parameters of a two- parameter geometric distribution under the general entropy loss, minimum expected loss and linex loss, functions for a noninformative as well as beta prior from multiply Type II censored data. We have studied the robustness of the estimators using simulation and we observed that the Bayes estimators of reliability and the parameters of a two-parameter geometric distribution under all the above loss functions appear to be robust with respect to the correct choice of the hyperparameters a(b) and a wrong choice of the prior parameters b(a) of the beta prior.

scholarly journals Estimation procedures on Type-II censored data from a scaled Muth distribution

2021 ◽  
pp. 148-158
Author(s):  
Hayrinisa Demirci BIÇER
Keyword(s):  
Censored Data ◽  
Mean Squared Error ◽  
Real Life ◽  
Model Parameters ◽  
Type Ii ◽  
Monte Carlo Simulation Study ◽  
Anal Ysis ◽  
Squared Error ◽  
Type Ii Censored Data ◽  
Censoring Scheme

In the present paper, we consider the estimation problem for the scaled Muth distribution under Type-II censoring scheme. In order to estimate the model parameters α and β, the maximum likelihood, the least-squares, and the maximum spacing estimators are derived. To show estimation efficiencies of the estimators obtained with this paper, we present an exten- sive Monte-Carlo simulation study in which the estimators are compared according to bias and mean squared error criteria. Furthermore, we evaluate the applicability of the scaled Muth distribution by taking into account both full and Type-II censored data situations by an anal- ysis conducted on a real-life dataset.

scholarly journals Bayesian Estimation of Entropy for Burr Type XII Distribution under Progressive Type-II Censored Data

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 313
Author(s):  
Xinjing Wang ◽  
Wenhao Gui
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Censored Data ◽  
Loss Functions ◽  
Type Ii ◽  
Important Indicator ◽  
Progressive Type ◽  
Type Ii Censored Data ◽  
Highest Posterior Density ◽  
Burr Type Xii

With the rapid development of statistics, information entropy is proposed as an important indicator used to quantify information uncertainty. In this paper, maximum likelihood and Bayesian methods are used to obtain the estimators of the entropy for a two-parameter Burr type XII distribution under progressive type-II censored data. In the part of maximum likelihood estimation, the asymptotic confidence intervals of entropy are calculated. In Bayesian estimation, we consider non-informative and informative priors respectively, and asymmetric and symmetric loss functions are both adopted. Meanwhile, the posterior risk is also calculated to evaluate the performances of the entropy estimators against different loss functions. In a numerical simulation, the Lindley approximation and the Markov chain Monte Carlo method were used to obtain the Bayesian estimates. In turn, the highest posterior density credible intervals of the entropy were derived. Finally, average absolute bias and mean square error were used to evaluate the estimators under different methods, and a real dataset was selected to illustrate the feasibility of the above estimation model.

Interval Estimation in Lifetime Distributions Using Progressively Type II Censored Data

2021 ◽  
Author(s):  
Ayman Baklizi
Keyword(s):  
Closed Form ◽  
Confidence Intervals ◽  
Censored Data ◽  
Interval Estimation ◽  
Real Data ◽  
Data Sets ◽  
Type Ii ◽  
Lifetime Distributions ◽  
Special Cases ◽  
Type Ii Censored Data

In this paper, we developed a method for constructing confidence intervals for the parameters of lifetime distributions based on progressively type II censored data. The method produces closed form expressions for the bounds of the confidence intervals for several special cases of parameters and lifetime distributions. Closed form approximations are derived for the intervals for the parameters of the location or scale families of distributions. The method is illustrated with several examples and analyses of real data sets are included to illustrate the application of the method.

Sign in / Sign up

Export Citation Format

Share Document