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Entropy
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Number Theoretic Methods in Statistics: Theory and Applications
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Number Theoretic Methods in Statistics: Theory and Applications

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 1860

Special Issue Editors

Prof. Kai-Tai Fang

E-Mail Website
Guest Editor
1. Institute of Applied Mathematics, Chinese Academy of Sciences, Zhuhai 519088, China
2. Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, Beijing Normal University—Hong Kong Baptist University United International College, Zhuhai 519087, China
Interests: design of experiments; applications of number theoretic methods in statistics; distribution theory including representative points of statistical distributions; multivariate analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yongdao Zhou

E-Mail Website
Guest Editor
School of Statistics and Data Science, Nankai University, Tianjin 300071, China
Interests: design of experiments; big data analysis

Special Issue Information

Dear Colleagues,

Number–theoretic methods (NTM) or quasi-Monte Carlo methods have played an important role in numerical integration in high dimensions, statistical inference, and experimental design, as well as having applications in engineering, biology, economics, and data science. This Special Issue will collate recent developments in NTM and its applications, including various kinds of representative points of distribution for statistical inference and resampling, including bootstrap.

Prof. Kai-Tai Fang
Prof. Dr. Yongdao Zhou
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • number–theoretic methods
  • quasi-Monte methods
  • experimental design
  • representative points
  • statistical inference
  • data science

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (3 papers)

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Research

28 pages, 1718 KiB  
Article
Advancing Continuous Distribution Generation: An Exponentiated Odds Ratio Generator Approach
by Xinyu Chen, Zhenyu Shi, Yuanqi Xie, Zichen Zhang, Achraf Cohen and Shusen Pu
Entropy 2024, 26(12), 1006; https://doi.org/10.3390/e26121006 - 22 Nov 2024
Viewed by 309
Abstract
This paper presents a new methodology for generating continuous statistical distributions, integrating the exponentiated odds ratio within the framework of survival analysis. This new method enhances the flexibility and adaptability of distribution models to effectively address the complexities inherent in contemporary datasets. The [...] Read more.
This paper presents a new methodology for generating continuous statistical distributions, integrating the exponentiated odds ratio within the framework of survival analysis. This new method enhances the flexibility and adaptability of distribution models to effectively address the complexities inherent in contemporary datasets. The core of this advancement is illustrated by introducing a particular subfamily, the “Type 2 Gumbel Weibull-G family of distributions”. We provide a comprehensive analysis of the mathematical properties of these distributions, including statistical properties such as density functions, moments, hazard rate and quantile functions, Rényi entropy, order statistics, and the concept of stochastic ordering. To test the robustness of our new model, we apply five distinct methods for parameter estimation. The practical applicability of the Type 2 Gumbel Weibull-G distributions is further supported through the analysis of three real-world datasets. These real-life applications illustrate the exceptional statistical precision of our distributions compared to existing models, thereby reinforcing their significant value in both theoretical and practical statistical applications. Full article
(This article belongs to the Special Issue Number Theoretic Methods in Statistics: Theory and Applications)
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24 pages, 1545 KiB  
Article
The Representative Points of Generalized Alpha Skew-t Distribution and Applications
by Yong-Feng Zhou, Yu-Xuan Lin, Kai-Tai Fang and Hong Yin
Entropy 2024, 26(11), 889; https://doi.org/10.3390/e26110889 - 22 Oct 2024
Viewed by 452
Abstract
Assuming the underlying statistical distribution of data is critical in information theory, as it impacts the accuracy and efficiency of communication and the definition of entropy. The real-world data are widely assumed to follow the normal distribution. To better comprehend the skewness of [...] Read more.
Assuming the underlying statistical distribution of data is critical in information theory, as it impacts the accuracy and efficiency of communication and the definition of entropy. The real-world data are widely assumed to follow the normal distribution. To better comprehend the skewness of the data, many models more flexible than the normal distribution have been proposed, such as the generalized alpha skew-t (GAST) distribution. This paper studies some properties of the GAST distribution, including the calculation of the moments, and the relationship between the number of peaks and the GAST parameters with some proofs. For complex probability distributions, representative points (RPs) are useful due to the convenience of manipulation, computation and analysis. The relative entropy of two probability distributions could have been a good criterion for the purpose of generating RPs of a specific distribution but is not popularly used due to computational complexity. Hence, this paper only provides three ways to obtain RPs of the GAST distribution, Monte Carlo (MC), quasi-Monte Carlo (QMC), and mean square error (MSE). The three types of RPs are utilized in estimating moments and densities of the GAST distribution with known and unknown parameters. The MSE representative points perform the best among all case studies. For unknown parameter cases, a revised maximum likelihood estimation (MLE) method of parameter estimation is compared with the plain MLE method. It indicates that the revised MLE method is suitable for the GAST distribution having a unimodal or unobvious bimodal pattern. This paper includes two real-data applications in which the GAST model appears adaptable to various types of data. Full article
(This article belongs to the Special Issue Number Theoretic Methods in Statistics: Theory and Applications)
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15 pages, 569 KiB  
Article
Maxpro Designs for Experiments with Multiple Types of Branching and Nested Factors
by Feng Yang and Zheng Zhou
Entropy 2024, 26(10), 856; https://doi.org/10.3390/e26100856 - 10 Oct 2024
Viewed by 632
Abstract
Contemporary experiments often involve special factors known as branching factors. The levels of such factors determine the presence of some certain factors, referred to as nested factors. The design criteria for investigating the goodness of such designs are rarely developed. Furthermore, the existing [...] Read more.
Contemporary experiments often involve special factors known as branching factors. The levels of such factors determine the presence of some certain factors, referred to as nested factors. The design criteria for investigating the goodness of such designs are rarely developed. Furthermore, the existing criteria for such designs pay less attention to the space-filling property of low-dimensional projections of the design. The efficiencies of designs yielded by such criteria can markedly decrease when only a few factors are significant. To address this issue, this paper proposes a novel space-filling criterion based on the maximum projection criterion to evaluate the performance of the designs with branching and nested factors. A framework to construct optimal designs under the proposed criterion is also provided. Compared with the existing works, the resulting designs have better space-filling properties in all possible low-dimensional projections. Moreover, our strategy imposes no constraints on run size, level, and type of any factor, demonstrating its broad applicability. Full article
(This article belongs to the Special Issue Number Theoretic Methods in Statistics: Theory and Applications)
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