A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data

Round 1

Reviewer 1 Report (Previous Reviewer 3)

Comments on “A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data (manuscript IDs 2303362 and 2399612)

Thank you for incorporating the reviewers' feedback into the manuscript. However, I have some concerns regarding the simulation study presented in Section 4.1. It is not entirely clear how the proposed WEW model outperforms other models when the data is not generated from Eq [6]. Table 1 merely demonstrates the consistency of the maximum likelihood estimates (MLEs) as the sample size increases without offering any novel insights.

The main question is whether the proposed WEW model can still provide a reasonable estimate of certain parameters of interest (such as the average length of time from admission to cure, or the probability of 5 or more days until cure) when the data is generated from a different distribution (e.g., GEW, EW, WW, etc.). If the answer is affirmative, then the application of the WEW distribution in Section 6 can be extended to a broader context, even if the underlying distribution of influenza and hepatitis data slightly deviates from the WEW distribution.

Good.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report (Previous Reviewer 1)

Dear Authors,

I have completed a careful review of your manuscript. I think your work improved considerably after making the adjustments suggested in previous reviews. However, some minor revisions remain in the manuscript that needs to be worked on before considering it for an eventual publication in Stats. They are listed below:

1. The quantity $p_{j,k}(b)$ used in equation 7 is defined in the Appendix. It should be defined in equation 7.

2. It is more informative for the reader to use the relative bias than the absolute bias in Tables 1 and 2.

3. For comparative purposes between models GEW and WEW, it is more appropriate to use the relative bias than the MSE in Figures 5 and 6.

4. The panel (a) Y-axis label in Figures 5 and 6 should be clarified.

5. A setup similar to section 6.2 should be included in section 5.2, i.e., n=30, and a censoring percentage of 66%.

Best Regard,

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report (New Reviewer)

The authors proposed a new distribution, named as extended Weibull distribution, and discussed its properties and applications.  I list my comments as follows,

1. The motivations for this manuscript are unclear, and the idea to generate the new distribution is straightforward, including the characteristics, which can be derived with some mathematical calculations. The authors need to address the unique significance for this proposed distribution, otherwise, there will be an infinite number of such new distributions.

2. There are two different aspects for the simulation, however, all the performances are not well, especially for the accuracy of the β and γ1 . You may need to use different estimation methods to obtain the more accuracy estimator. 

3. In the table 1, the data set are generated from the WEW distribution, and why did the comparison with the GEW distribution? I think the simulation work here is to verify the accuracy of the estimator. 

4. In table 2, as the censoring percentages increased, the accuracy for the estimators turn to be worse, how to explain these results? And how to fix them? In your simulation, did you avoid this situation? 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report (New Reviewer)

Thank you for the response.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The authors propose a new distribution called Weibull extended Weibull with applications to influenza and hepatitis data. Some mathematical properties are also derived. Although I believe it is important to apply new and more flexible probabilistic models to data like those proposed by the authors, major revisions to the manuscript are necessary before it can be reconsidered for publication in Stats. My main comments are listed below:

1. Regarding the Abstract: it needs improvement as it does not adequately summarize the work. For example, the regression model is not even mentioned.

2. The keywords should be different from those used in the paper's title.

3. The introduction should be rephrased, particularly concerning: i) An update on the bibliographic references, mainly on extensions of the Weibull distribution, models obtained by the Weibull-G family, and more recent models used to explain influenza and hepatitis data; ii) A stronger motivation for the gap in the literature that the new distribution aims to solve.

4. The mathematical properties of the model should be discussed and expanded. For example, what happens to the mean of X? What other properties can be derived? In the linear representation of Section 3.2, the mathematical procedures can be included in an Appendix section. Instead, it would be interesting to comment on the importance and practical applications of that representation.

5. I find the estimation section weak. It is important to include more details on estimation and other alternative methods. I suggest that the score vector be included and details be presented on the estimation of the model parameters from the Bayesian approach as an alternative method.

6. In the Simulation Study section, I strongly suggest that the simulated scenarios correspond to the same scenarios as in Figure 1. This is to understand how the estimation works in different possible shapes assumed by the density function.

7. A simulation study for the regression model should be included. Note that the regression model is applied to a set of twenty-nine data points, and nothing is known about estimates of the parameters of the regression model in small samples.

8. Results obtained through the new distribution and its associated regression model are missing from the paper. It should be discussed whether the results of the proposed models are in line with the literature.

9. The conclusion needs to be improved. It is written as a brief summary but does not provide conclusive comments on the paper's results.

10. The source codes used should be made available to the reader. This can be done through the GitHub platform.

Author Response

Por favor, verifique o anexo.

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors,

Extension of well-known distributions appears to be a good idea to match the multi-modal behavior.

I recommend the publication of your manuscript.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments on "A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data" (Manuscript ID: stats-2303362)

Here are a few comments:

[1]. The simulation study section explores the properties of the MLE under different sample sizes, but did not investigate its properties when the underlying distribution is unknown, i.e., the data are not generated from Equation (4).  It would be more insightful if data are simulated from other distributions and a comparison of the resulting MLEs between the proposed model and some competing models can be made.

[2]. In Table 2. are the numbers in parenthesis the p-values or SEs? 

[3]. (Page 1, Line 18) Perhaps change the random variable "W" to "X" to be consistent with the variables used in the formulas and the rest of the manuscript.

Author Response

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Author Response File: Author Response.pdf