Simultaneous Confidence Intervals for All Pairwise Differences between Means of Weibull Distributions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

    I really enjoyed reviewing the text entitled "Simultaneous confidence Intervals for all pairwise differences between means of Weibull distributions". It is a scientific sound manuscript, which gives the impression of being very well planned, written in a fluent and understandable way. I start by highlighting the Abstract, truly an Abstract, short and with complete information. Next we have the Introduction in which the authors give the essential concepts for the development of the text, and present very clearly the objective of the study they are going to undertake, all of this based on an excellent review of the literature, very informative and enlightening. They end the Introduction with a description of the structure of the remainder of the text, much more complete than is usual, in which they generally describe the results they will obtain. This way of proceeding, different from what is usual, makes it easier for readers to follow and understand the text. In the two sections that follow, the subject of the manuscript is developed, mathematically very well aligned, with the results presented followed by texts that clarify their meaning and point to their possible use in solving problems.

    I would highlight here the great importance of the proposed simultaneous confidence intervals for all pairwise differences between means of Weibull distributions. In addition, generalized confidence interval, method of variance estimates recovery, and a Bayesian approach utilizing both gamma and uniform prior distributions are proposed to construct simultaneous confidence intervals. Through simulations, the authors found that the Bayesian highest posterior density interval using a gamma prior distribution demonstrates satisfactory performance. These proposed approaches applied to real wind speed data in northeastern Thailand to illustrate their effectiveness and practicality.

    The conclusions are presented in a clear and assertive way, with the authors emphasizing the different fields in which their results are applicable. I think that, as the manuscript is mathematical in nature, the authors should indicate at least one MSC. Having said that, I have no doubt in recommending the publication of this manuscript in Symmetry.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

See the attached file please.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

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Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Authors,

 

The evaluation of various methods, such as GCI, MOVER, and a Bayesian approach, emphasizes the Bayesian Highest Posterior Density (HPD) interval with a gamma prior as a recommended option for constructing confidence intervals. The application of suggested methods, including GCI, MOVER, and Bayesian approaches, to actual wind speed data in northeastern Thailand demonstrates their effectiveness and applicability. Simulations demonstrate satisfactory performance of the Bayesian HPD interval using a gamma prior, while the GCI proves to be a feasible alternative.

 

 

Typos and Suggestions:

 

-Put keywords in alphabetical order;

-Page 3, line 100: substitute “Let a_io is the observed…” by  “Let a_io be the observed…”

-Page 3, line 102: substitute “are the maximum…” by  “be the maximum …”

-Page 4, line 124: l_i  and u_i must be defined here and not on page 5, line 150, because it appears before on page 4, line 124;

-Page 4, line 133: explain the meaning of the sentence: “The MOVER, which was……”;

-Page 5, section 2.3., Please substitute: “The Bayesian” by “Bayesian Inference”; and explain in detail why the authors used a gamma prior distribution. The authors explain that is to accomplish Bayesian inference. But explain in detail if there are other prior distributions and why you must use this prior distribution;

-Page 5, line 167, and line 179 are in contradiction?? Please clarify;

-Page 6, line 194: “Furthermore, we are interested….” explain the sentence and the meaning;

-Page 7, line 251: why do not consider the same number of simulations?

-Page 10, line 291: where is the link for the data used? Which data are used? Explain in detail and give the link to the data;

 

 

In the manuscript limitations of the Bayesian HPD interval for small sample sizes are acknowledged, urging further consideration in future research. Please add some solutions and explain what you intend to do.

 

Also, the absence of specific details regarding sample sizes in simulations and real data analysis is emphasized as an area for improvement.

 

The authors propose three approaches - Generalized Confidence Interval (GCI), Method of Variance Estimates Recovery (MOVER), and a Bayesian approach using gamma and uniform prior distributions. Can you give us more details about more approaches? And why they are different and useful?

 

 

 Kind Regards

Author Response

Please see attached

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Dear authors,

After careful review, you have effectively addressed the feedback and improved the overall quality of the manuscript.

Kind Regards