scholarly journals Bayesian Estimation of Shape Parameter and Failure Rate from Burrxii Distribution under Progressive Type-Ii Censored Data

2016 ◽  
Vol 06 (04) ◽  
pp. 307-311
Author(s):  
慧敏 余
Keyword(s):  
Bayesian Estimation ◽  
Failure Rate ◽  
Censored Data ◽  
Shape Parameter ◽  
Type Ii ◽  
Progressive Type ◽  
Type Ii Censored Data

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 Bayesian Estimation of Entropy for Burr Type XII Distribution under Progressive Type-II Censored Data

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 313
Author(s):  
Xinjing Wang ◽  
Wenhao Gui
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Censored Data ◽  
Loss Functions ◽  
Type Ii ◽  
Important Indicator ◽  
Progressive Type ◽  
Type Ii Censored Data ◽  
Highest Posterior Density ◽  
Burr Type Xii

With the rapid development of statistics, information entropy is proposed as an important indicator used to quantify information uncertainty. In this paper, maximum likelihood and Bayesian methods are used to obtain the estimators of the entropy for a two-parameter Burr type XII distribution under progressive type-II censored data. In the part of maximum likelihood estimation, the asymptotic confidence intervals of entropy are calculated. In Bayesian estimation, we consider non-informative and informative priors respectively, and asymmetric and symmetric loss functions are both adopted. Meanwhile, the posterior risk is also calculated to evaluate the performances of the entropy estimators against different loss functions. In a numerical simulation, the Lindley approximation and the Markov chain Monte Carlo method were used to obtain the Bayesian estimates. In turn, the highest posterior density credible intervals of the entropy were derived. Finally, average absolute bias and mean square error were used to evaluate the estimators under different methods, and a real dataset was selected to illustrate the feasibility of the above estimation model.

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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