Application of Continuous Non-Gaussian Mortality Models with Markov Switchings to Forecast Mortality Rates
Round 1
Reviewer 1 Report
1) Please revise the title rather than FORECAST μx,t
2) The novelty of this paper is not very clear. Would you please add the novelty of the work either in abstract or in conclusion which differs from literature?
3) Please review more relevant works and find the research gap from there and as a short paragraph at the end of literature.
4) A general high level block diagram or framework of complete work in this paper is required to add at the beginning of chapter 2 so that readers can follow up the entire technical work has been done in this paper.
5) Performance/advantages comparison with existing related works would be good add at the end of result section to validate the capability of the proposed method presented in the paper.
6) You have provided the MSE however, 95% confidence interval for different nGon is missing.
7) ergodic distribution could also be provided.
8) Discussion part need to be expanded with more critical analysis and discussion about the values of the mortality rates: empirical values, theoretical values and forecasts based on the nG model.
9) Please add impact/significance of this work in real life scenarios.
10) Specific Future research directions are missing. Please add those at the end of conclusions.
Author Response
Dear Reviewer,
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Please correct page 18 lines -10,-9, and -8 as:
Among these situations, how
can we study Hyers-Ulam-Rassias and Hyers-Ulam stability of some fractional differential equations \cite{a,b} with Caputo derivative \cite{c,d}?
[a] El-hady, El-sayed, Öğrekçi, Süleyman. "On Hyers-Ulam-Rassias stability of fractional differential equations with Caputo derivative." Journal of Mathematics and Computer Science, 22, no. 4 (2021): 325--332.
[b] Alghamdi, Maryam, Aljehani, Alaa, Hamza, Alaa E. "Hyers-Ulam-Rassias stability of abstract second-order linear dynamic equations on time scales." Journal of Mathematics and Computer Science, 24, no. 2 (2022): 110--118.
[c] Maazouz, Kadda; Rodríguez-López, Rosana. Differential equations of arbitrary order under Caputo-Fabrizio derivative: some existence results and study of stability. Math. Biosci. Eng. 19 (2022), no. 6, 6234--6251.
[d] Wang, Shuyi. The Ulam stability of fractional differential equation with the Caputo-Fabrizio derivative. J. Funct. Spaces 2022, Art. ID 7268518, 9 pp.
Author Response
Dear Reviewer 2,
We thank You for Your comments.
Point 1. Please correct page 18 lines -10,-9, and -8 as: Among these situations, how can we study Hyers-Ulam-Rassias and Hyers-Ulam stability of some fractional differential equations \cite{a,b} with Caputo derivative \cite{c,d}?
[a] El-hady, El-sayed, Öğrekçi, Süleyman. "On Hyers-Ulam-Rassias stability of fractional differential equations with Caputo derivative." Journal of Mathematics and Computer Science, 22, no. 4 (2021): 325--332.
[b] Alghamdi, Maryam, Aljehani, Alaa, Hamza, Alaa E. "Hyers-Ulam-Rassias stability of abstract second-order linear dynamic equations on time scales." Journal of Mathematics and Computer Science, 24, no. 2 (2022): 110--118.
[c] Maazouz, Kadda; Rodríguez-López, Rosana. Differential equations of arbitrary order under Caputo-Fabrizio derivative: some existence results and study of stability. Math. Biosci. Eng. 19 (2022), no. 6, 6234--6251.
[d] Wang, Shuyi. The Ulam stability of fractional differential equation with the Caputo-Fabrizio derivative. J. Funct. Spaces 2022, Art. ID 7268518, 9 pp.
Response 1: In our opinion this is a misunderstanding, because:
- our original version of the article posted on 11 May contained only 17 pages, so we cannot complete page 18,
- moreover, our proposed way of modelling mortality rates is not related to fractional differential equations.
Reviewer 3 Report
This study proposed a method of modeling the mortality rates u_x,t with different time intervals of higher and lower dispersion. Overall, the manuscript is interesting; however, the following issues should be addressed before the final publication.
1. For Section 1, the authors should provide the comments of the cited papers after introducing each relevant work. What readers require is, by convinced literature review, to understand the clear thinking/consideration of why the proposed approach can reach more convincing results. This is the very contribution from the authors.
2. There are some grammatical mistakes and typos. In addition, the writing style can also be improved. For example, the sentence "For the second part of the empirical data, it is proposed a model of Markov switched models for the first and third part of the observed data." can be improved.
3. At the end of section 1, please provide the structure of the manuscript.
4. Provide details about the data used in the analysis section. It would be better to plot it separately.
5. The first line of the abstract refers to the pandemic; however, the data used in this study is till 2016. How has this model been tasted in recent pandemic years? Please clarify within the text as well.
6. Why did the author not consider other age groups? It would be interesting to see the performance of their proposed models for all age groups.
7. Looking at table 1, it is not very clear how the models are performing. The differences in the MSEs are extremely small as the MSE's values are extremely small. Thus, the author's claim of the best results from their models is not reasonable.
8. In addition, the authors should perform some statistical tests to assess the significance of differences (if any) in the results listed in Table 1.
9. The authors should compare their results with other existing models. There are many models that can produce very good results.
Author Response
Dear Reviewer,
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
1. Regarding the tile please replace μx,t this by a general terminology.
2. Regarding the previous comment no 4, I was asking to add the steps of the technical work not asking for structure of the article. This comment has not been addressed.
3. Regarding the previous point 6, please add a separate table with CI for the forecasts for few years rather than each calendar year.
Author Response
Dear Reviewer 1,
We thank You very much for Your next comments. Please find below our corrections and explanations.
Point 1. Regarding the tile please replace μx,t this by a general terminology.
Response 1: We have modified the title as follows:
APPLICATION OF CONTINUOUS NON-GAUSSIAN MORTALITY MODELS WITH MARKOV SWITCHINGS TO FORECAST MORTALITY RATES
Point 2. Regarding the previous comment no 4, I was asking to add the steps of the technical work not asking for structure of the article. This comment has not been addressed.
Response 2: We have added at the end of the section Introduction the steps of the technical work.
Point 3. Regarding the previous point 6, please add a separate table with CI for the forecasts for few years rather than each calendar year.
Response 3: We have added Table 2 with CI for a nG2 model, and nGs model.
Author Response File: Author Response.pdf
Reviewer 2 Report
I suggest the authors provide a section about the fractional equations and apply the following results [a] Chalishajar, Dimplekumar; Ramkumar, K.; Anguraj, A.; Ravikumar, K.; Diop, Mamadou Abdoul. Controllability of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion with infinite delay via resolvent operator. J. Nonlinear Sci. Appl. 15 (2022), no. 3, 172--185.
[b]Ahmed, Hamdy M., El-Borai, Mahmoud M., El-Owaidy, H. M., Ghanem, A. S.. "Null controllability of fractional stochastic delay integro-differential equations." Journal of Mathematics and Computer Science, 19, no. 3 (2019): 143--150
Author Response
Dear Reviewer 2,
We thank You for Your next suggestions.
Point 1. I suggest the authors provide a section about the fractional equations and apply the following results
[a] Chalishajar, Dimplekumar; Ramkumar, K.; Anguraj, A.; Ravikumar, K.; Diop, Mamadou Abdoul. Controllability of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion with infinite delay via resolvent operator. J. Nonlinear Sci. Appl. 15 (2022), no. 3, 172--185.
[b]Ahmed, Hamdy M., El-Borai, Mahmoud M., El-Owaidy, H. M., Ghanem, A. S.. "Null controllability of fractional stochastic delay integro-differential equations." Journal of Mathematics and Computer Science, 19, no. 3 (2019): 143—150.
Response 1: In our opinion this suggestion require an additional work on the mortality models described by the fractional equations, which was not discussed in the literature yet. In a previous version of our manuscript we have already added a suggestion regarding future works about applying fractional equations to the mortality models. At this moment we are not experts in the field of the fractional equations and therefore we may only expect that this modern mathematical tool can be used in the study of mortality models. Therefore we have not introduced new changes to the previous version of the manuscript.
Author Response File: Author Response.pdf
Reviewer 3 Report
The authors largely addressed my concerns and hence, I recommend the paper for publication in its present form.
Author Response
Dear Reviewer 3,
We thank You for accepting the revisions we have introduced to the manuscript.
Author Response File: Author Response.pdf
