E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data

Round 1

Reviewer 1 Report

The work deals with the E-Bayesian estimation in specific situuations of censoting sheme. The work is interesting and well presented. In my opinion I should improve some aspects that I briefly detail:

1.- The last paragraph on page 2 should be revised and expanded. It does not specify in detail the applications that are cited or justify the opportunity to quote them.

2.- The reason for the selection of gamma function as prior is not justified. It is true that this is usually the case, but in this case it is precisely the intention to improve the classical approach that option seems incongruous. Clarify

3.- The Markovian option is not justified and the discrete processes over time present a series of added complications that are ignored here.

4.- Review the MSE calculation expressions (page 8).

5.- Much of the coclusions are evident. Clarify that it is provided beyond what is widely known (page 13)

Author Response

Thanks a lot for your valuable comments, all comments have been done.

Author Response File: Author Response.pdf

Reviewer 2 Report

I put the comments and suggestions. please, see it.

Comments for author File: Comments.pdf

Author Response

Thank you for your valuable comments, all comments have been considered.

Author Response File: Author Response.pdf

Reviewer 3 Report

In this paper, the authors compare the E-Bayesian (expectation of the Bayesian estimate) method and the corresponding Bayesian and maximum likelihood methods of the parameter and the reliability function of Burr-X distribution.  The authors considered the generalized Type-II hybrid censored sample from Burr-X distribution case.  

The authors used two different loss functions:  LINEX and squared error loss functions. Moreover, since there is not analytical solution they rely on Markov chain Monte Carlo techniques. The authors computed confidence intervals for the maximum likelihood estimates as well as credible intervals for Bayesian and E-Bayesian estimates.

The authors used real data sets to illustrate or compare the results of the different methods. The authors concluded that the performance of the E-Bayesian method is better than the corresponding Bayesian and maximum likelihood methods.

The article is interesting and could be useful for other scientists working on the area since the Burr distribution is not well-known but can be applied in health sciences, biology and agriculture.. Some issues that need to be improved before publication are the following:

·         Explain what means LINEX for the readers who are not aware.

·         Line 84. Expand the phrase “The algorithm is proposed as follows” . For what ?

·         Line 104. Explain why the authors chose in particular 11000 and 1000 values ?

·         Tables. Explain better them. For instance, EBS1, EBS2, EBS3… EBL1, EBL2. More important the number index.

·         Conclusions: Some results were expected in terms of the sample size and time points. The authors need to explain why the LINEX gives better results than the SEL loss function. This happens always ? explain.

·         Authors concluded that E-Bayesian is better than ML and Bayesian methods. Explain why this happens. Always this is the case ?

·         Add or mention some drawbacks of the E-Bayesian method.

Author Response

Thank you very much for your valuable comments, all comments have been done.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have improved the work and properly resolved my previous observations.