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 A Mixture of Two Burr Type III Distributions: Identifiability and Estimation under Type II Censoring

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
A. S. Al-Moisheer
Keyword(s):  
Monte Carlo Simulation ◽  
Real Data ◽  
Reliability Function ◽  
Type Ii ◽  
Estimation Technique ◽  
Numerical Illustration ◽  
Data Set ◽  
Type Ii Censoring ◽  
Type Iii ◽  
Statistical Library

The mixture of two Burr Type III distributions (MTBIIID) is investigated. First, the identifiability property of the MTBIIID is proved. Then, two different methods of estimation are used. Next, the estimates of the unknown five parameters and reliability function of the MTBIIID under Type II censoring are obtained. To study the performance of the estimation technique in the paper, a Monte Carlo simulation is presented. In addition, the numerical illustration requires solving nonlinear equations; therefore, the software international mathematical statistical library (IMSL) is used to assess these effects numerically. Finally, a real data set is applied to illustrate the methods proposed here.

scholarly journals Estimation and Testing Procedures for the Reliability Characteristics of Chen Distribution Based on Type II Censoring and the Sampling Scheme of Bartholomew

2020 ◽  
Vol 9 (1) ◽  
pp. 99-122
Author(s):  
Aditi Chaturvedi ◽  
Surinder Kumar
Keyword(s):  
Real Data ◽  
Point Estimation ◽  
Sampling Scheme ◽  
Type Ii ◽  
Data Set ◽  
Testing Procedures ◽  
Type Ii Censoring ◽  
Reliability Characteristics ◽  
Two Measures ◽  
Parametric Functions

In this paper, we consider Chen distribution and derive UMVUEs and MLEs of the parameter λ , hazard rate h(t) and the two measures of reliability, namely R(t) = P(X > t), where X denotes the lifetime of an item and P = P(X > Y ), which represents the reliability of an item or system of random strength X subject to random stress Y , under type II censoring scheme and the sampling scheme of Bartholomew . We also develop interval estimates of the reliability measures. Testing procedures for the hypotheses related to different parametric functions have also been developed. A comparative study of different methods of point estimation and average confiddence length has been done through simulation studies. The analysis of a real data set is presented for illustration purpose.

scholarly journals Statistical inferences with jointly type-II censored samples from two Pareto distributions

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 557-565 ◽  
Author(s):  
Hanaa H. Abu-Zinadah
Keyword(s):  
Confidence Intervals ◽  
Life Time ◽  
Model Parameters ◽  
Type Ii ◽  
Time Data ◽  
Data Set ◽  
Censored Samples ◽  
Credible Intervals ◽  
Life Tests ◽  
Censoring Scheme

AbstractIn the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method.

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 Exact Likelihood Inference for a Competing Risks Model with Generalized Type II Progressive Hybrid Censored Exponential Data

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 887
Author(s):  
Subin Cho ◽  
Kyeongjun Lee
Keyword(s):  
Competing Risks ◽  
Real Data ◽  
Likelihood Inference ◽  
Type Ii ◽  
Conditional Moment ◽  
Data Set ◽  
Scale Parameters ◽  
Competing Risks Model ◽  
Censoring Scheme ◽  
Generalized Type

In many situations of survival and reliability test, the withdrawal of units from the test is pre-planned in order to to free up testing facilities for other tests, or to save cost and time. It is known that several risk factors (RiFs) compete for the immediate failure cause of items. In this paper, we derive an inference for a competing risks model (CompRiM) with a generalized type II progressive hybrid censoring scheme (GeTy2PrHCS). We derive the conditional moment generating functions (CondMgfs), distributions and confidence interval (ConfI) of the scale parameters of exponential distribution (ExDist) under GeTy2PrHCS with CompRiM. A real data set is analysed to illustrate the validity of the method developed here. From the data, it can be seen that the conditional PDFs of MLEs is almost symmetrical.

scholarly journals Maximum likelihood estimation based on type-i hybrid progressive censored competing risks data

2016 ◽  
Vol 4 (1) ◽  
pp. 20
Author(s):  
Samir Ashour ◽  
Wael Abu El Azm
Keyword(s):  
Maximum Likelihood ◽  
Competing Risks ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Data Set ◽  
Special Cases ◽  
Competing Risks Data

<p>This paper is concerned with the estimators problems of the generalized Weibull distribution based on Type-I hybrid progressive censoring scheme (Type-I PHCS) in the presence of competing risks when the cause of failure of each item is known. Maximum likelihood estimates and the corresponding Fisher information matrix are obtained. We generalized Kundu and Joarder [7] results in the case of the exponential distribution while, the corresponding results in the case of the generalized exponential and Weibull distributions may be obtained as a special cases. A real data set is used to illustrate the theoretical results.</p>

scholarly journals Different Approaches to Estimation of the Gompertz Distribution under the Progressive Type-II Censoring Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Kyeongjun Lee ◽  
Jung-In Seo
Keyword(s):  
Nuisance Parameter ◽  
Estimation Method ◽  
Real Data ◽  
Type Ii ◽  
Gompertz Distribution ◽  
Type Ii Censoring ◽  
Scale Parameters ◽  
Progressive Type ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

This paper provides an estimation method for an unknown parameter by extending weighted least-squared and pivot-based methods to the Gompertz distribution with the shape and scale parameters under the progressive Type-II censoring scheme, which induces a consistent estimator and an unbiased estimator of the scale parameter. In addition, a way to deal with a nuisance parameter is provided in the pivot-based approach. For evaluation and comparison, the Monte Carlo simulations are conducted, and real data are analyzed.

scholarly journals Competing Risks Model with Partially Step-Stress Accelerate Life Tests in Analyses Lifetime Chen Data under Type-II Censoring Scheme

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 192-199 ◽  
Author(s):  
Hanaa H. Abu-Zinadah ◽  
Neveen Sayed-Ahmed
Keyword(s):  
Risk Factors ◽  
Risk Model ◽  
Asymptotic Distributions ◽  
Likelihood Method ◽  
Model Parameters ◽  
Type Ii ◽  
Monte Carlo Simulation Study ◽  
Type Ii Censoring ◽  
Life Tests ◽  
Censoring Scheme

Abstract The experiment design may need a stress level higher than use condition which is called accelerate life tests (ALTs). One of the most ALTs appears in different applications in the life testes experiment is partially step stress ALTs. Also, the experiment items is failure with several fatal risk factors, the only one is caused to failure which called competing risk model. In this paper, the partially step-stress ALTs based on Type-II censoring scheme is adopted under the different risk factors belong to Chen lifetime distributions. Under this assumption, we will estimate the model parameters of the different causes with the maximum likelihood method. The two, asymptotic distributions and the parametric bootstrap will be used to build each confidence interval of the model parameters. The precision results will be assessed through Monte Carlo simulation study.

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