The Confluent Hypergeometric Beta Distribution
Round 1
Reviewer 1 Report
The article is well written and would be in a position to be accepted after the authors respond to the following suggestions:
i) They should arrange the article in such a way that several tests of the results are left in an appendix.
ii) The authors found a closed form for the cumulative distribution function, they can add the hazard function.
ii) They can add a second application and compare it with other distributions.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
Dear Authors,
I have completed a careful review of your manuscript. I think it would be worth making some minor corrections to the manuscript before its eventual publication in Mathematics. They are listed below:
1. A correction is necessary for lines 31 and 32. The distribution shown in equation (1) does not depend on parameter d.
2. I think it would be helpful for the reader to include Monte Carlo simulations by choosing a scenario from each panel of Figure 1. I think it would be interesting to see the estimates' behavior for different density shapes.
3. Since the maximum likelihood estimators do not have a closed form, I believe the methods used in 11 and 12 for the solution of the non-linear system should be mentioned in the text.
Author Response
Please see attached.
Author Response File: Author Response.pdf
Reviewer 3 Report
In this work, the authors provided a systematic study of the
confluent hypergeometric beta distribution is given by a probability density function that was defined in Goordy 1998. In fact, the authors present a comprehensive study of the mathematical properties of the properties derived including the shape properties of the probability density function, cumulative distribution function, moment generating, characteristic functions...etc
This work is worthy and interesting, the presented results are mathematically correct and the presentation of the paper is good. However, the authors require to read their manuscript carefully and correct some minor language.
I recommend this paper for publication after minor revision.
In this work, the authors provided a systematic study of the
confluent hypergeometric beta distribution is given by a probability density function that was defined in Goordy 1998. In fact, the authors present a comprehensive study of the mathematical properties of the properties derived including the shape properties of the probability density function, cumulative distribution function, moment generating, characteristic functions...etc
This work is worthy and interesting, the presented results are mathematically correct and the presentation of the paper is good. However, the authors require to read their manuscript carefully and correct some minor language.
I recommend this paper for publication after minor revision.
Author Response
Please see attached.
Author Response File: Author Response.pdf
Reviewer 4 Report
REVIEW
of the paper: The confluent hypergeometric beta distribution
by Saralees Nadarajah and Malick Kebe presented for publishing in journal Mathematics
The present study contains an original analysis of confluent hypergeometric beta distribution.
The properties derived include the shape properties of the probability density function (Section 2), cumulative distribution function (Section 3), moment generating and characteristic functions (Section 4), moments (Section 5), conditional moments (Section 6), entropies (Section 7) and stochastic orderings (Section 8).
The authors also derive procedures for maximum likelihood estimation (Section 9) and assess their finite sample performance (Section 10).
A real data application of the confluent hypergeometric beta distribution is illustrated in Section 11.
Some conclusions and future work are also given.
In this regard, I have the following question: do the authors intend to consider the "composite" beta distributions in the light, for example, of the considerations for other distributions, see e.g. Zaevski, T., N. Kyurkchiev, On some composite Kies families: distributional properties and saturation in Hausdorff sense, Modern Stochastics: Theory and Applications (2023)
The advantages of this distribution have been used very successfully in conducting numerous statistical tests to analyze the empirical data.
The authors, compare the performance of the confluent hypergeometric beta distribution with the standard beta distribution using a real data set. The data are the winner’s share of the electoral college vote for the United States presidential elections from 1824 to 2016.
The article is very well structured, contains interesting results and opens up opportunities for further research in this scientific direction.
This gives me reason to recommend the paper “The confluent hypergeometric beta distribution “ by Saralees Nadarajah and Malick Kebe for publishing in J. Mathematics.
English language is fine.
Author Response
Please see attached.
Author Response File: Author Response.pdf
