Goodness-of-Fit Tests for Weighted Generalized Quasi-Lindley Distribution Using SRS and RSS with Applications to Real Data
Round 1
Reviewer 1 Report
In this manuscript, the problem of goodness-of-fit tests (GFT) for the weighted generalized quasi-Lindley distribution (WGKLD) is considered. Using various statistical tests (& techniques), authors demonstrate the advantages of the ranked set sampling (RSS) technique over simple random sampling (SRS). The topic of the manuscript itself, as the whole mathematical & statistical "apparatus" used here, is not too big. Still, authors give a lot of attention and effort to extensive simulations, which seem to really show the advantage of the RSS-method. Also, the manuscript is concise and clearly written, with a practical application of GFT that seems very interesting. Therefore, my opinion regarding this manuscript is positive, and above all I think that the special issue "Computational Mathematics and Mathematical Physics" suits it. Therefore, I propose to consider the manuscript as acceptable for publication, with a few (mainly technical and methodological) remarks as follows:
1. Line 13: Section numbers should be renumbered (so that "Introduction" is the first section). This omission is seen in the description of the contents of the manuscript in Lines 58-63.
2. Lines 83-84: The part of the sentence "...while the imperfect ranking may be considered in the future works" is not necessary.
3. Lines 170-172: The first comment is not entirely clear and should be changed, as well as the values in the tables where positive power estimates of order e-04 appear. These "small" values should be adequately displayed, for instance, using the (standard "R") notation "<1e-03", or similar.
4. Lines 212-214: I am not sure how accurate this sentence is, and in any case it is too long and vague. I think it is much better to simply add the p-values for each test statistic in Table 8. In that way, the reader would have a clearer understanding of the author's comments given here.
5. Line 237: "Abbreviations" are not necessary, because there are not too many abbreviations in the manuscript itself and they are all entered correctly. (However, I leave it to the authors to decide for themselves whether to accept this proposal.)
Author Response
Dear Reviewer
The authors would like to thank you for valuable and constructive comments that improved the paper. In what follows we answer their requests, point-by-point.
Best regards
Author Response File: 
Author Response.docx
Reviewer 2 Report
In this work the authors continue researching the features of Weighted generalized Quasi Lindley distribution (WGQLD), which they have proposed before in [20]. Now they study the properties of various goodness-of-fit tests with application to this distribution. Critical values for different sample size and sampling methods are obtained by numerical simulation.
In fact this is a technical work. It does not introduce new ideas or methods, it's main result is tabulating values for WGQLD. These values can be useful for other researchers in case they select WGQLD as a model of some data under study.
However, the authors should persuade reader that WGQLD is better than rivals in modeling something from real life. More real data studies are necessary and comparison with rivals is advisable. In this work only one sample of rain data is presented, and it is stated that the hypothesis that these data belong to WGQLD is not rejected. Very well, but why anyone should prefer WGQLD rather than any of other known distributions, which also pass the tests.
Other aspects are good: mathematics, structure, presentation.
Author Response
Dear Reviewer
The authors would like to thank you for valuable and constructive comments that improved the paper. In what follows we answer their requests, point-by-point.
Best regards
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
The authors have added two more samples of real data and comparative tests of their method and SOTA methods. This is good, although second sample is very small.
However, now there is a greater flaw in the text. In Tables 7-9 there p-values are shown. The authors do not explain what do they mean by 'p-value', so the standard understanding is applied. At first, p-value is not an independent characteristic of distribution, it refers to some statistics over this distribution. It is unclear what statistics p-value is referred to. Well, consider that p-value is given for KS statistics. (Why not give it for all others then?). Second, null hypothesis is the statement "There is no relation in observed real data which is described by WGQLD distribution". Alternative: "Real data are described by WGQLD". For instance, considering table 7 this will sound as: "If real data are not interrelated by WGQLD, we will obtain KS=0.06 or more extremal with probability of 0.866". This makes WGQLD useless since null hypothesis cannot be rejected. Third, after table 9 the authors claim that maximum p-value for WGQLD is best. In fact, standard understanding of p-value is just the opposite: smaller is better. The authors should carefully reconsider this issue.
Author Response
Dear Reviewer
The authors would like to thank you for valuable and constructive comments that improved the paper. In what follows we answer their requests, point-by-point.
Best regards
Author Response File: Author Response.docx
Round 3
Reviewer 2 Report
The authors have modified the paper so as to explain and clarify the previously given comment. However the p-values in tables 7-9 still cause perplexing. The p-value for their method is everywhere above 0.4 and competing methods have it always below 0.04. The difference is by a factor of ten and more. This looks like as WGQLD is really brilliant against its rivals. Are these rivals really so poor in approximating the data? What is the reason of this uncompromised victory of WGQLD over its rivals, say, its closest relative QLD? I think this questions can be answered by adding CDF and PDF graphs for rival methods in figure 3. This is done in the papers cited in the cover letter (Aldahlan20 figures 6-7, ZeinEldin19 figures 9-12) and it really supports the tabulated KS p-vales. It is also worth noting, that in these papers p-values of proposed methods and its rivals are the same order or magnitude, rather than differing in ten or hundred times.
Author Response
Dear Reviewer
The authors would like to thank you for valuable and constructive comments that improved the paper. In what follows we answer their requests, point-by-point. The new modifications are in blue font.
Best regards
Author Response File: Author Response.docx
