Classical and Bayesian estimation for type-I extended-F family with an actuarial application

Nada M. Alfaer; Sarah A. Bandar; Omid Kharazmi; Hazem Al-Mofleh; Zubair Ahmad; Ahmed Z. Afify

doi:10.1371/journal.pone.0275430

Peer Review History

Original SubmissionAugust 5, 2022
23 Aug 2022 Decision Letter - Srinivasa Rao Gadde, Editor PONE-D-22-21984Classical and Bayesian Estimation for Type-I Extended-F Family with an Actuarial ApplicationPLOS ONE Dear Dr. Afify, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please submit your revised manuscript by Oct 07 2022 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. 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The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf 2. We note that the grant information you provided in the ‘Funding Information’ and ‘Financial Disclosure’ sections do not match. When you resubmit, please ensure that you provide the correct grant numbers for the awards you received for your study in the ‘Funding Information’ section. 3. Please ensure that you refer to Figures 4 to 6 in your text as, if accepted, production will need this reference to link the reader to the figure. 4. We note you have included a table to which you do not refer in the text of your manuscript. Please ensure that you refer to Tables 1, 2, 6, 8, 9, and 10 in your text; if accepted, production will need this reference to link the reader to the Table. 5. Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. Additional Editor Comments: Dear Author, Please revise and submit the manuscript. Remember that you have to respond to all comments given the reviewers. Please prepare response matrix for each reviewers and revised manuscript within 10 days. with best wishes [Note: HTML markup is below. Please do not edit.] Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes Reviewer #2: Partly Reviewer #3: Yes ******** 2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: Yes Reviewer #3: Yes ****** 3. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #1: Yes Reviewer #2: Yes Reviewer #3: Yes ****** 4. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: No Reviewer #2: Yes Reviewer #3: Yes ****** 5. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: 1.The introduction must be separate from the methodology 2.The conclusion must be well written and organized 3.Some tables do not cite; they must be cited (“The parameters estimate …. Table??. The goodness… in Table??.”) 4.An acronym must be added. 5.The writing style of the manuscript have been not follow the guidelines 6.The discussion part is essential. But not written in the manuscript 7.Resnick, S.I. (1997). Discussion of the Danish data on large fire insurance losses. 268 ASTIN Bulletin: The Journal of the IAA, 27, 139-151.not urgent 8.McNeil, A. J. (1997). Estimating the tails of loss severity distributions using 261 extreme value theory. ASTIN Bulletin: The Journal of the IAA, 27(1), 117-137: not urgent Reviewer #2: This study proposes a new family of distributions named Type-I Extended-F Family (TIEx-F) with a specific focus on modelling insurance data. Some properties and numerous classical and Bayesian estimation approaches are introduced for estimating the parameters of a special case, the TIEx-Weibull (TIEx-W) model. Finally, the author demonstrate the potentials of the model by applying it to a single insurance datasets. The authors have performed a good job, however, I have some issues and suggestions that may enhance the current version of the manuscript. See the attached file for the comments Reviewer #3: The authors have put in considerable effort in explaining their research aim and finding but need to add some comments on the tables and charts rather than leaving them blank. The functional for of the estimators should also be provided even if he procedure can be verified by readers. ****** 6. 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Revision 1
7 Sep 2022 Author Response Response Letter Respected Editor Enclosed herewith are the pdf and latex files of the revised version of our paper entitled "Classical and Bayesian Estimation for Type-I Extended-F Family with an Actuarial Application ", which we hope you will find now satisfactory. First, we would like to thank the Editor and three reviewers for his very constructive comments. In the revised version all suggestions and comments have been taken into account and addressed. All corrections and modifications are incorporated in the revised version and highlighted in magenta color. We now answer the comments made by the Editor and the three reviewers in the order they appeared in the reports. Journal Requirements: When submitting your revision, we need you to address these additional requirements. 1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf Answer: We have prepared the paper according to PLOS ONE's style requirements. 2. We note that the grant information you provided in the ‘Funding Information’ and ‘Financial Disclosure’ sections do not match. When you resubmit, please ensure that you provide the correct grant numbers for the awards you received for your study in the ‘Funding Information’ section. Answer: Thanks. We corrected them. 3. Please ensure that you refer to Figures 4 to 6 in your text as, if accepted, production will need this reference to link the reader to the figure. Answer: We double checked and cited all figures and tables in the text. 4. We note you have included a table to which you do not refer in the text of your manuscript. Please ensure that you refer to Tables 1, 2, 6, 8, 9, and 10 in your text; if accepted, production will need this reference to link the reader to the Table. Answer: We double checked and cited all figures and tables in the text. 5. Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. Answer: Thanks for this comment. We have removed two references as suggested by Reviewer #1. Some references has been added in the application section (Section 7) because we have added some new models in the application to compare them with the TIEx-W model as suggested by Reviewer #2. All changes in the revised version are highlighted in magenta color. Reviewers' comments: Reviewer #1: 1. The introduction must be separate from the methodology. Answer: Thanks for this suggestion. We have improved accordingly. We have added a new section entitled ‘’The TIEx-F Family’’. 2. The conclusion must be well written and organized. Answer: Thanks for this suggestion. The conclusion section is corrected accordingly. 3. Some tables do not cite; they must be cited (“The parameters estimate …. Table??. The goodness… in Table??.”) Answer: Thanks for careful reading. All tables and figures are now cited in the text. 4. An acronym must be added. Answer: Thanks for this comment. We have added a list of abbreviations at the end of the paper. 5. The writing style of the manuscript have been not follow the guidelines. Answer: We have double checked and improved the writing style throughout the paper. 6. The discussion part is essential. But not written in the manuscript. Answer: Thanks for this comment. We have improved the conclusion section to include the discussion as you suggested in your Comment #2. 7. Resnick, S.I. (1997). Discussion of the Danish data on large fire insurance losses. 268 ASTIN Bulletin: The Journal of the IAA, 27, 139-151. not urgent 8. McNeil, A. J. (1997). Estimating the tails of loss severity distributions using 261 extreme value theory. ASTIN Bulletin: The Journal of the IAA, 27(1), 117-137: not urgent. Answer: Thanks for this suggestion. We have removed the two references. Reviewer #2: This study proposes a new family of distributions named Type-I Extended-F Family (TIEx-F) with a specific focus on modelling insurance data. Some properties and numerous classical and Bayesian estimation approaches are introduced for estimating the parameters of a special case, the TIEx-Weibull (TIEx-W) model. Finally, the authors demonstrate the potentials of the model by applying it to a single insurance dataset. The authors have performed a good job; however, I have some issues and suggestions that may enhance the current version of the manuscript. There should be more clear motivation of the study. Answer: Many thanks for this comment. We have improved the motivation accordingly. Please see the introduction section. The authors refer the TIExF family "the most tractable for simple analytical expressions" with TIEx-W as a special case, I expect the authors to assess the TIEx-W with other competing non-standard distributions, such as the special cases derived from families defined in Equations (1)-(3). Going by this will explore more the potentials of the proposed family. Answer: Thanks for this comment. We add the following special case derived from families defined in Equations (1)-(3): APTW, AmpaduAPTW and ExAPTW. We have also added some competing models. Please see Table 6. Check the correctness of the sentence and citations in page 3, lines 55-56. Answer: This sentence is checked and corrected. The authors should provide the other basic functions of the TIEx-W distribution, including the survival and hazard rate functions, along with plot(s) showing some possible shapes of the hazard rate function for different settings of the model's parameters. Also present some discussions on the plots and whether the hazard rate function is relevant in modelling insurance data. Answer: Thanks for this suggestion. We have provided the required discussions, functions, figures, and discussions. Please see Equations (8) and (9), and Figure 2. In section 3, more properties of the distribution should be present not only the quantile function and moments. Answer: Thanks for this comment. We have provided some more properties such as the quantile function, median, shapes of TIEx-W pdf and the order statistics, please see sub-sections 4.2, 4.4 and 4.5. Do your quantile function has a closed form expression? If yes, please, write it clearly, and if no, provide a procedure on how to draw random sample from the quantile function. Answer: Thanks for your comment. Yes, the quantile function has a closed form expression, we provided it in Equation (10) for the TIEx-F family and in Equation (11) for the TIEx-W model. Table numbers are missing in the text. Check and correct it. Answer: Thanks for careful reading. We have checked and corrected them. Check and correct the third term of Eq. (15). Not correctly differentiated. Answer: Thanks for your comment. We have double checked Equation (15). It is correct. We have just moved this term ‘’e^(-γx_k^α )’’ from the numerator ‘’e^(-γx_k^α )’’ to the denominator to be e^(γx_k^α ). In section 5, I suggest the authors to include simulation results for the Bayesian approach under the selected loss functions to enable the comparison of all the proposed estimators for the TIEx-W model. Answer: Thanks for this comment. It is well-known that the Bayesian estimators are better than classical estimators follow using classical methods of estimation. Hence, your suggestion will be a good point for a future paper. In this future work, we may propose the Bayes estimators of the parameters of the TIEx-W distribution for complete and censored samples under different loss functions. We can also use different approximation techniques to obtain the Bayes estimates of the parameters. In section 7, discuss the reasons/justifications for choosing gamma priors for the three parameters of TIEx-W model. Answer: Thanks for this comment. It is well-known that the gamma priors provide flexible approach to handle estimation procedure in both informative and non-informative. The authors need to provide some discussions on the Bayesian results. Answer: Thanks for this comment. We have provided the required discussion. I also expect to see some comparisons between the results from the classical estimation methods and the Bayesian results either by plotting the density curves, CDF curves for the trained TIEx-W model from all the estimation methods employed or the p-p plots. This is essential to identify the best estimation method(s) in solving real-world problems. Answer: Thanks for this comment. We have provided a new table which includes the estimates of the TIEx-W parameters using all estimation methods. We have also provided the density plots and PP plots for all methods. How the estimated values of the parameters can be translated in the real-life situations? Answer: Thanks for this comment. Our aim is to show the flexibility of the proposed TIEx-W distribution in modelling insurance data. Based on the fitted TIEx-W model, we can answer some questions such as the probability of having more than X claims per day. Reviewer #3: The authors have put in considerable effort in explaining their research aim and finding but need to add some comments on the tables and charts rather than leaving them blank. The functional for of the estimators should also be provided even if the procedure can be verified by readers. Answer: Thanks for this comment. We have provided the required comments about tables and figures. The functions for all proposed estimators are provided in the paper. We have also added some new results as suggested by the two other reviewers. Attachments Attachment Submitted filename: Response-Letter_PLOS ONE.pdf https://doi.org/10.1371/journal.pone.0275430.r002
19 Sep 2022 Decision Letter - Srinivasa Rao Gadde, Editor Classical and Bayesian Estimation for Type-I Extended-F Family with an Actuarial Application PONE-D-22-21984R1 Dear Dr. Afify, We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org. If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. Kind regards, Srinivasa Rao Gadde, Ph.D. Academic Editor PLOS ONE Additional Editor Comments (optional): The author has responded all my comments as well as reviewer's comments. No new comments. Reviewers' comments: https://doi.org/10.1371/journal.pone.0275430.r003
Formally Accepted
29 Sep 2022 Acceptance Letter - Srinivasa Rao Gadde, Editor PONE-D-22-21984R1 Classical and Bayesian Estimation for Type-I Extended-F Family with an Actuarial Application Dear Dr. Afify: I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org. If we can help with anything else, please email us at plosone@plos.org. Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staff on behalf of Professor Srinivasa Rao Gadde Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0275430.r004

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