Knowable Moments in Stochastics: Knowing Their Advantages

Round 1

Reviewer 1 Report

The paper is a detailed review of the K-moments theory. The advantages of these moments are presented and supported by numerous examples. The results obtained can be really useful for reconstructing the probability density function for stochastic variables.

I can recommend the manuscript for publication after some minor corrections:

The manuscript can be shortened by eliminating some repetitions of the same sentences and self-citations. For example, the same expression is represented in lines 419, 420, 422 and 488.

In the revised version, some typos should be corrected and punctuation marks should be added after the equations.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Review of manuscript

Knowable Moments in Stochastics: Knowing their Advantages

by Demetris Koutsoyiannis

General comment:

This paper focus on knowable moments (k-moments) defined as expectations of maxima or minima of a number of random variables.

1.      The main work is limited to the illustration of individual examples, there are no deeper theoretical insights.  

2.      The presented methodology is well known from the author's previous publications.

3.      Nothing author present here is new. However, from experience, author have found that a simple and compact guide on this matter written for the hydrology community is missing.

4.      The abstract and introduction does not emphasize the novelty of the work and its contribution to the field of mathematics.

5.      The introduction does not discuss the differences between this work and the studies of maximum value distributions and quantile regression.

6.      The references are mainly composed of the works of the author.

7.      Notations (such as random variable, etc.) and concepts used should follow a well-established structure in mathematics.

8.      The mathematics-oriented, high-level scientific journal "Axioms" requires substantial mathematical meaning of the presented articles.

The article is written in acceptable language.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

There are some concerns to improve the presented article and suggested methodologies and strategies. They are:

1. Authors should explain how the concept of "knowable moments" used in this paper differs from other types of stochastic variables, and how this distinction affects the properties of the probability density function. 

2. Authors should provide a concrete example of a knowable moment and demonstrate how the results of this paper can be applied to it.

3. Authors discuss the potential implications of the results obtained in this paper for applications in other areas of applied mathematics, and how they can be used to solve open problems or improve existing models.  

4. The authors should discuss the computational complexity of the derived conditions. Moreover, the authors should give the architecture of the proposed model.

5. The language of this should be improved. There are many grammar mistakes in the text.

6. What is the main contribution of this paper to the field of Knowable Moments in Stochastics? Authors should show the point-wise.

7. How does the paper relate to the existing literature on this topic, and What is the limitation of your proposed model? Are there other ways that the results can be further improved? One or two remarks should be given to discuss it in detail.

Nil

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors answered all the questions. The writing is acceptable. The paper can be accepted.

The writing is acceptable

Reviewer 3 Report

The revised version is satisfied. May be it can be acceptable.

Nil