Robust Mixture Modeling Based on Two-Piece Scale Mixtures of Normal Family

Round 1

Reviewer 1 Report

- summary

In this paper, the authors considered the finite mixture (FN) of the two-piece scale mixtures of normal (TP-SMN) family for 1-dimensional data analysis. The FN-TP-SMN is useful for robust estimation for skewed distributions. The EM-based algorithm is proposed for parameter estimation. In numerical experiments, the proposed model showed competitive performance to the existing models. 

- review

This is an interesting paper. After minor revision, the article is worthwhile for publication from Axioms journal. 

comments:

It is not very clear what is precisely the main contribution of this paper. Did Arellano-Valle et al. (2005) and Maleki and Mahmoudi (2017) already propose the TP-SMN model? In my understanding, the authors of this paper proposed the finite mixture of the TP-SMN and the EM-like algorithm for parameter estimation. A clear comment about that would be nice. In Table 1, FM-TP-CN outperforms the other methods when the true model is FM-TP-T. Supplementing some comments on it would improve the paper. 

Author Response

The authors would like to thank Editor and the reviewers for providing constructive comments, encouragement and suggestions. All the comments are considered, and the paper has been revised accordingly. The changes/corrections are highlighted in yellow color in the revised version. Also, some typographical, grammatical and punctuation errors are highlighted (yellow) in the revised file.

Response to Reviewer 1:

This is an interesting paper. After minor revision, the article is worthwhile for publication from Axioms journal. 

Comments:

It is not very clear what is precisely the main contribution of this paper. Did Arellano-Valle et al. (2005) and Maleki and Mahmoudi (2017) already propose the TP-SMN model? In my understanding, the authors of this paper proposed the finite mixture of the TP-SMN and the EM-like algorithm for parameter estimation. A clear comment about that would be nice. In Table 1, FM-TP-CN outperforms the other methods when the true model is FM-TP-T. Supplementing some comments on it would improve the paper. 

R: First of all, we greatly appreciate your encouragement and the important suggestions given for improving the manuscript. As you have said, Arellano-Valle et al. (2005) and Maleki and Mahmoudi (2017) considered the TP-SMN model and we have considered the finite mixtures of the TP-SMN (i.e. FM-TP-SMN) model. Then, we used the EM-like algorithm for parameter estimation. Also according your suggestion we have added your note at lines 235-236 (yellow highlighted).

Reviewer 2 Report

The manuscript contains information worthy of publication. However, there are some typos in the manuscript that should be corrected. Some examples are:

- abstract, fist line, ``wo-piece" should be ``two-piece"

- abstract, line 6, ``two piece" should be ``two-piece" with a hyphen

- Section two, title, remove the hyphen

- page 7 (line 180), the equation number is better to go to the very right-hand side

Although the paper contains some merits, the conclusion section is poor and does not emphasize the importance of the work.

Author Response

The authors would like to thank Editor and the reviewers for providing constructive comments, encouragement and suggestions. All the comments are considered, and the paper has been revised accordingly. The changes/corrections are highlighted in yellow color in the revised version. Also, some typographical, grammatical and punctuation errors are highlighted (yellow) in the revised file.

Response to Reviewer 2:

The manuscript contains information worthy of publication. However, there are some typos in the manuscript that should be corrected. Some examples are:

- abstract, fist line, ``wo-piece" should be ``two-piece"

- abstract, line 6, ``two piece" should be ``two-piece" with a hyphen

- Section two, title, remove the hyphen

- page 7 (line 180), the equation number is better to go to the very right-hand side

Although the paper contains some merits, the conclusion section is poor and does not emphasize the importance of the work.

Response: First of all, we greatly appreciate your encouragement and the important suggestions given for improving the manuscript. We have corrected the typos errors. According your valuable suggestion, we have rewritten the conclusion part to emphasizing the importance of work.