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.

scholarly journals Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 264 ◽  
Author(s):  
M. El-Morshedy ◽  
Ziyad Ali Alhussain ◽  
Doaa Atta ◽  
Ehab M. Almetwally ◽  
M. S. Eliwa
Keyword(s):  
Real Data ◽  
Bivariate Distribution ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Sets ◽  
Type Ii ◽  
Censored Samples ◽  
Type Ii Censored Data ◽  
Modeling Data

Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate extension of the BX-G family, in the so-called bivariate Burr X-G (BBX-G) family of distributions based on the Marshall–Olkin shock model. Important statistical properties of the BBX-G family are obtained, and a special sub-model of this bivariate family is presented. The maximum likelihood and Bayesian methods are used for estimating the bivariate family parameters based on complete and Type II censored data. A simulation study was carried out to assess the performance of the family parameters. Finally, two real data sets are analyzed to illustrate the importance and the flexibility of the proposed bivariate distribution, and it is found that the proposed model provides better fit than the competitive bivariate distributions.

MCMC in Analysis of Progressively First Failure Censored Competing Risks Data for Gompertz Model

2016 ◽  
Vol 13 (10) ◽  
pp. 6662-6670 ◽  
Author(s):  
R. A Bakoban ◽  
G. A Abd-Elmougod
Keyword(s):  
Confidence Intervals ◽  
Competing Risks ◽  
Life Time ◽  
Real Data ◽  
Asymptotic Distributions ◽  
Type Ii ◽  
Data Set ◽  
Type Ii Censoring ◽  
Gamma Density ◽  
Special Cases

In medical studies or in reliability analysis, it is quite common that the failure of any individual or any item may be attributable to more than one cause. So in this paper, we consider the competing risks model with very general censoring scheme, namely progressive first-failure censored scheme under the Gompertz life time distribution. The results in each of first-failure censoring, progressive Type II censoring, Type II censoring and complete sample are a special cases. We provide different methods for the analysis of the model under the assumption of independent causes of failure and Gompertz distribution lifetimes. The maximum likelihood estimators (MLE’s) of the different parameters as well as approximate confidence intervals are presented. Bayesian estimation using MCMC method under the joint prior density as a product of a conditional gamma density and inverted gamma density for unknown Gompertz parameters are presented. The analysis of a real data set to assess the performance of all these estimators, confidence intervals are developed using asymptotic distributions and Bayesian credible intervals for the parameters. The different methods are compared through a simulation study.

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 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.

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