Inference for the reliability function based on progressively type II censored data from the Pareto model: The generalized variable approach

2018 ◽  
Vol 343 ◽  
pp. 275-288 ◽  
Author(s):  
Sumith Gunasekera
Keyword(s):  
Censored Data ◽  
Reliability Function ◽  
Type Ii ◽  
Variable Approach ◽  
Pareto Model ◽  
Type Ii Censored Data ◽  
Generalized Variable Approach

scholarly journals Bayesian Estimation Based on Rayleigh Progressive Type II Censored Data with Binomial Removals

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Reza Azimi ◽  
Farhad Yaghmaei
Keyword(s):  
Censored Data ◽  
Failure Time ◽  
Simulation Method ◽  
Reliability Function ◽  
Rayleigh Distribution ◽  
Type Ii ◽  
Monte Carlo Simulation Method ◽  
Bayesian Procedures ◽  
Progressive Type ◽  
Type Ii Censored Data

This study considers the estimation problem for the parameter and reliability function of Rayleigh distribution under progressive type II censoring with random removals, where the number of units removed at each failure time has a binomial distribution. We use the maximum likelihood and Bayesian procedures to obtain the estimators of parameter and reliability function of Rayleigh distribution. We also construct the confidence intervals for the parameter of Rayleigh distribution. Monte Carlo simulation method is used to generate a progressive type II censored data with binomial removals from Rayleigh distribution, and then these data are used to compute the point and interval estimations of the parameter and compare both the methods used with different random schemes.

scholarly journals Minimum Variance Unbiased Estimation in the Gompertz Distribution under Progressive Type II Censored Data with Binomial Removals

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Ashok Shanubhogue ◽  
N. R. Jain
Keyword(s):  
Censored Data ◽  
Hazard Function ◽  
Shape Parameter ◽  
Reliability Function ◽  
Minimum Variance ◽  
Unbiased Estimation ◽  
Type Ii ◽  
Gompertz Distribution ◽  
Progressive Type ◽  
Type Ii Censored Data

This paper deals with the problem of uniformly minimum variance unbiased estimation for the parameter of the Gompertz distribution based on progressively Type II censored data with binomial removals. We have obtained the uniformly minimum variance unbiased estimator (UMVUE) for powers of the shape parameter and its functions. The UMVUE of the variance of these estimators is also given. The UMVUE of (i) pdf, (ii) cdf, (iii) reliability function, and (iv) hazard function of the Gompertz distribution is derived. Further, an exact % confidence interval for the th quantile is obtained. The UMVUE of pdf is utilized to obtain the UMVUE of . An illustrative numerical example is presented.

scholarly journals Model Selection Approaches for Predicting Future Order Statistics from Type II Censored Data

2018 ◽  
Vol 2018 ◽  
pp. 1-29
Author(s):  
Jyun-You Chiang ◽  
Shuai Wang ◽  
Tzong-Ru Tsai ◽  
Ting Li
Keyword(s):  
Model Selection ◽  
Order Statistics ◽  
Censored Data ◽  
Model Misspecification ◽  
Extreme Value Distribution ◽  
Type Ii ◽  
Underlying Distribution ◽  
Censored Samples ◽  
Scale Family ◽  
Type Ii Censored Data

This paper studies a discriminant problem of location-scale family in case of prediction from type II censored samples. Three model selection approaches and two types of predictors are, respectively, proposed to predict the future order statistics from censored data when the best underlying distribution is not clear with several candidates. Two members in the location-scale family, the normal distribution and smallest extreme value distribution, are used as candidates to illustrate the best model competition for the underlying distribution via using the proposed prediction methods. The performance of correct and incorrect selections under correct specification and misspecification is evaluated via using Monte Carlo simulations. Simulation results show that model misspecification has impact on the prediction precision and the proposed three model selection approaches perform well when more than one candidate distributions are competing for the best underlying distribution. Finally, the proposed approaches are applied to three data sets.

Estimation of P(X

2017 ◽  
Vol 34 (7) ◽  
pp. 1111-1122 ◽  
Author(s):  
Soumya Roy ◽  
Biswabrata Pradhan ◽  
E.V. Gijo
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Quality Characteristic ◽  
Logistic Distribution ◽  
Type Ii ◽  
Finite Sample ◽  
Data Set ◽  
Content Type ◽  
Type Ii Censored Data ◽  
Interval Estimators

Purpose The purpose of this paper is to compare various methods of estimation of P(X<Y) based on Type-II censored data, where X and Y represent a quality characteristic of interest for two groups. Design/methodology/approach This paper assumes that both X and Y are independently distributed generalized half logistic random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator of R are obtained based on Type-II censored data. An exact 95 percent maximum likelihood estimate-based confidence interval for R is also provided. Next, various Bayesian point and interval estimators are obtained using both the subjective and non-informative priors. A real life data set is analyzed for illustration. Findings The performance of various point and interval estimators is judged through a detailed simulation study. The finite sample properties of the estimators are found to be satisfactory. It is observed that the posterior mean marginally outperform other estimators with respect to the mean squared error even under the non-informative prior. Originality/value The proposed methodology can be used for comparing two groups with respect to a suitable quality characteristic of interest. It can also be applied for estimation of the stress-strength reliability, which is of particular interest to the reliability engineers.

scholarly journals Estimating the Parameters of the Exponential-Geometric distribution based on progressively type-II censored data

2018 ◽  
Vol 6 (1) ◽  
pp. 37
Author(s):  
Aisha Fayomi ◽  
Hamdah Al-Shammari
Keyword(s):  
Censored Data ◽  
Geometric Distribution ◽  
Asymptotic Variance ◽  
Parameters Estimation ◽  
Type Ii ◽  
Progressive Type ◽  
The Em Algorithm ◽  
Asymptotic Confidence Intervals ◽  
Distribution Parameters ◽  
Type Ii Censored Data

This paper deals with the problem of parameters estimation of the Exponential-Geometric (EG) distribution based on progressive type-II censored data. It turns out that the maximum likelihood estimators for the distribution parameters have no closed forms, therefore the EM algorithm are alternatively used. The asymptotic variance of the MLEs of the targeted parameters under progressive type-II censoring is computed along with the asymptotic confidence intervals. Finally, a simple numerical example is given to illustrate the obtained results.

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