Simple Approximations and Interpretation of Pareto Index and Gini Coefficient Using Mean Absolute Deviations and Quantile Functions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Here are some comments and suggestions for the authors:

1. Clarify the derivation of the methods: While the formulas are simplified and easily understandable, it would be helpful to include a more detailed explanation of their derivation, especially for readers less familiar with numerical quadrature approximations. Adding a diagram or illustration of the quadrature approach could enhance comprehension.

2. Empirical validation with real data: The simulation analysis is convincing, but applying these methods to actual datasets from diverse sources (e.g., socio-economic data, tax records) would strengthen the demonstration of their effectiveness in practical scenarios.

3. Extension to other distributions: You mention potential extensions to other commonly used distributions. It would be beneficial to outline a possible approach or methodology for these extensions, or to specify particular distributions (e.g., log-normal, Weibull) to guide future work.

4. Discussion of limitations: While robustness against outliers is demonstrated for the Pareto case, further discussion on potential limitations or situations where these methods might face challenges—such as with very small samples or extreme data imbalances—would be valuable.

5. Practical implementation example: Including a detailed, step-by-step example of applying the formulas to a sample dataset would enhance the practical utility of your approach and assist readers in understanding and adopting the methods.

6. Additional references: Incorporating recent or complementary references on robust estimation techniques, especially within economic or financial contexts, could enrich the theoretical discussion and situate your contributions within current research trends.

Comments on the Quality of English Language

The language is professional and generally clear; however, minor grammatical adjustments, ensuring consistency, and enhancing sentence clarity would improve overall readability and polish.

Author Response

Thank you for your helpful suggestions. Please see the enclosed file with our responses

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Hello Authors 

Good efforts to put this paper together. Your manuscript is generally sound and has the potential to contribute to literature. However, consider my minor comments to improve it further.

INTRODUCTION: 

I suggest you reduce the citations and maintain most relevant ones to enhance readability and proper flow. Could you please highlight or make the research gap more clearer? For instance, what are lacking in terms of policy or theoretical implications of existing studies that are germane and cannot be overlooked, and this paper seeks to address? Let this be obvious,  straightforward, and concise. 

CONCLUSION:

I suggest you expand this section by briefly summarizing and discussing the findings to a layperson's understanding so that the work would be useful beyond econometricians. Let's the takeaways be clear. Please before you suggest future research direction, briefly highlight the limitation of your study for which a future study is necessary. Did you anticipate another research gap that should be examined by future researchers? Be specific in your suggestions. 

Good luck! 

Author Response

Thank you for your helpful advice and suggestions. Please see our responses in the enclosed file

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I am attaching my review report in pdf file format.

Comments for author File: Comments.pdf

Author Response

Thank you for your advice and suggestions. Please see our responses in the attached file

Author Response File: Author Response.pdf