Monitoring the Weibull Shape Parameter with Type II Censored Data

2014 ◽  
Vol 31 (5) ◽  
pp. 741-760 ◽  
Author(s):  
Yin Chan ◽  
Bing Han ◽  
Francis Pascual
Keyword(s):  
Censored Data ◽  
Shape Parameter ◽  
Type Ii ◽  
Type Ii Censored Data

scholarly journals Bayesian using Importance Sampling Technique of Weibull Regression with Type II Censored Data

2021 ◽  
Vol 2 (3) ◽  
pp. 10-18
Author(s):  
Mohammed Ahmed Al omari
Keyword(s):  
Importance Sampling ◽  
Censored Data ◽  
Shape Parameter ◽  
Sampling Technique ◽  
Type Ii ◽  
Jeffreys Prior ◽  
Weibull Regression ◽  
Type Ii Censored Data ◽  
The Mean ◽  
Importance Sampling Technique

Keeping in view the Bayesian approach, the study aims to develop methods through the utilization of Jeffreys prior and modified Jeffreys prior to the covariate obtained by using the Importance sampling technique. For maximum likelihood estimator, covariate parameters, and the shape parameter of Weibull regression distribution with the censored data of Type II will be estimated by the study. It is shown that the obtained estimators in closed forms are not available, but through the usage of appropriate numerical methods, they can be solved. The mean square error is the criterion of comparison. With the use of simulation, performances of these three estimates are assessed, bearing in mind different censored percentages, and various sizes of the sample.

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.

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