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 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 Bayesian Estimation for Inverse Weibull Distribution Under Progressive Type-II Censored Data With Beta-Binomial Removals

2018 ◽  
Vol 47 (1) ◽  
pp. 77-94
Author(s):  
Pradeep Kumar Vishwakarma ◽  
Arun Kaushik ◽  
Aakriti Pandey ◽  
Umesh Singh ◽  
Sanjay Kumar Singh
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Estimation Procedure ◽  
Type Ii ◽  
Unknown Parameters ◽  
Data Set ◽  
Progressive Type ◽  
Inverse Weibull Distribution ◽  
Type Ii Censored Data ◽  
Censoring Scheme

This paper deals with the estimation procedure for inverse Weibull distribution under progressive type-II censored samples when removals follow Beta-binomial probability law. To estimate the unknown parameters, the maximum likelihood and Bayes estimators are obtained under progressive censoring scheme mentioned above. Bayes estimates are obtained using Markov chain Monte Carlo (MCMC) technique considering square error loss function and compared with the corresponding MLE's. Further, the expected total time on test is obtained under considered censoring scheme.  Finally, a real data set has been analysed to check the validity of the study.

scholarly journals Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 566-571
Author(s):  
Rana A. Bakoban
Keyword(s):  
Exponential Distribution ◽  
Coefficient Of Variation ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Interval Estimate ◽  
Type Ii ◽  
Bayesian Approaches ◽  
Data Set ◽  
Type Ii Censored Data ◽  
Censoring Scheme

AbstractThe coefficient of variation [CV] has several applications in applied statistics. So in this paper, we adopt Bayesian and non-Bayesian approaches for the estimation of CV under type-II censored data from extension exponential distribution [EED]. The point and interval estimate of the CV are obtained for each of the maximum likelihood and parametric bootstrap techniques. Also the Bayesian approach with the help of MCMC method is presented. A real data set is presented and analyzed, hence the obtained results are used to assess the obtained theoretical results.

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 On the Omega Distribution: Some Properties and Estimation

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 656
Author(s):  
Abdelaziz Alsubie ◽  
Zuber Akhter ◽  
Haseeb Athar ◽  
Mahfooz Alam ◽  
Abd EL-Baset A. Ahmad ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Type Ii ◽  
Data Set ◽  
Simulation Results ◽  
Censoring Scheme ◽  
Single And Product Moments

We obtain explicit expressions for single and product moments of the order statistics of an omega distribution. We also discuss seven methods to estimate the omega parameters. Various simulation results are performed to compare the performance of the proposed estimators. Furthermore, the maximum likelihood method is adopted to estimate the omega parameters under the type II censoring scheme. The usefulness of the omega distribution is proven using a real data set.

scholarly journals Estimating E-Bayesian of Parameters of Inverse Weibull Distribution Using an Unified Hybrid Censoring Scheme

2021 ◽  
pp. 113-122
Author(s):  
Shahram Yaghoobzadeh Shahrastani ◽  
Iman Makhdoom
Keyword(s):  
Monte Carlo Simulation ◽  
Real Data ◽  
Bayesian Estimator ◽  
Type I ◽  
Type Ii ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Inverse Weibull Distribution ◽  
Censoring Scheme

The combination of generalization Type-I hybrid censoring and generalization Type-II hybrid censoring schemes, scheme creates a new censoring called a Unified hybrid censoring scheme. Therefore, in this study, the E-Bayesian estimation of parameters of the inverse Weibull (IW) distribution is obtained under the unified hybrid censoring scheme, and the efficiency of the proposed method was compared with the Bayesian estimator using Monte Carlo simulation and a real data set.

scholarly journals Bayesian and E-Bayesian Estimations of Bathtub-Shaped Distribution under Generalized Type-I Hybrid Censoring

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 934
Author(s):  
Yuxuan Zhang ◽  
Kaiwei Liu ◽  
Wenhao Gui
Keyword(s):  
Bayesian Method ◽  
Real Data ◽  
Loss Functions ◽  
Type I ◽  
Statistical Efficiency ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Bayesian Estimations ◽  
Generalized Type

For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.

scholarly journals Exact Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censored Competing Risks Data

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2005
Author(s):  
Youngseuk Cho ◽  
Kyeongjun Lee
Keyword(s):  
Risk Model ◽  
Moment Generating Function ◽  
Conditional Moment ◽  
Exponential Parameter ◽  
Exact Inference ◽  
Scale Parameters ◽  
Lower Confidence Bound ◽  
Competing Risks Data ◽  
Conditional Moment Generating Function ◽  
Censoring Scheme

It is known that the lifetimes of items may not be recorded exactly. In addition, it is known that more than one risk factor (RisF) may be present at the same time. In this paper, we discuss exact likelihood inference for competing risk model (CoRiM) with generalized adaptive progressive hybrid censored exponential data. We derive the conditional moment generating function (ConMGF) of the maximum likelihood estimators of scale parameters of exponential distribution (ExpD) and the resulting lower confidence bound under generalized adaptive progressive hybrid censoring scheme (GeAdPHCS). From the example data, it can be seen that the PDF of MLE is almost symmetrical.

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