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Symmetry
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Research Topics Related to Skew-Symmetric Distributions
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Research Topics Related to Skew-Symmetric Distributions

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 9528

Special Issue Editors

Prof. Dr. Toshihiro Abe

E-Mail Website
Guest Editor
Department of Economics, Hosei University, Tokyo, Japan
Interests: EM/MM algorithm; flexible modeling; skew-symmetric distributions
Prof. Dr. Kunio Shimizu

E-Mail Website
Guest Editor
The Institute of Statistical Mathematics, Tokyo, Japan
Interests: directional statistics; discrete distributions
Dr. Tomoaki Imoto

E-Mail Website
Guest Editor
School of Management and Information, University of Shizuoka, Shizuoka, Japan
Interests: directional statistics; discrete distributions; multivariate distributions

Special Issue Information

Dear Colleagues,

In diverse scientific fields, symmetric distributions are applied for many statistical analyses because of their mathematical and statistical tractability. However, the phenomenon in a real dataset is not always symmetric, and thus "symmetric" requirement for the underlying distributions is too restrictive and sometimes provides a wrong insight into the observations. For this reason, there has been increasing interest in the flexible skew distributions in recent years.

This Special Issue of Symmetry focuses on the studies and methodologies of the skew distributions as well as symmetric distributions. Statistical inference and applications based on the flexible distribution are welcome. In addition to these topics, Bayesian inference and examples of applications of those theories are also welcome.

Prof. Dr. Toshihiro Abe 
Prof. Dr. Kunio Shimizu
Dr. Tomoaki Imoto
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. Symmetry 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 2400 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

  • Bayesian inference
  • data analysis
  • flexible modelling
  • multivariate analysis
  • skew distributions
  • statistical modelling and inference

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Published Papers (6 papers)

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Research

20 pages, 673 KiB  
Article
Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions
by Yoichi Miyata, Takayuki Shiohama and Toshihiro Abe
Symmetry 2024, 16(3), 295; https://doi.org/10.3390/sym16030295 - 3 Mar 2024
Viewed by 993
Abstract
A class of cylindrical distributions, which include the Weibull-von Mises distribution as a special case, is considered. This distribution is obtained by combining the extended sine-skewed wrapped Cauchy distribution (marginal circular part) with the Weibull distribution (conditional linear part). This family of proposed [...] Read more.
A class of cylindrical distributions, which include the Weibull-von Mises distribution as a special case, is considered. This distribution is obtained by combining the extended sine-skewed wrapped Cauchy distribution (marginal circular part) with the Weibull distribution (conditional linear part). This family of proposed distributions is shown to have simple normalizing constants, easy random number generation methods, explicit moment expressions, and identifiability in parameters. In particular, the marginal distribution of the circular random variable, and its conditional distribution given a linear random variable give relatively stronger skewness than those of existing cylindrical models. Some Monte Carlo simulations and real data analysis are performed to investigate the feasibility and tractability of the proposed models. Full article
(This article belongs to the Special Issue Research Topics Related to Skew-Symmetric Distributions)
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15 pages, 2129 KiB  
Article
g.ridge: An R Package for Generalized Ridge Regression for Sparse and High-Dimensional Linear Models
by Takeshi Emura, Koutarou Matsumoto, Ryuji Uozumi and Hirofumi Michimae
Symmetry 2024, 16(2), 223; https://doi.org/10.3390/sym16020223 - 12 Feb 2024
Viewed by 2216
Abstract
Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to [...] Read more.
Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to non-uniform shrinkage; this was shown to perform well in sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package “g.ridge” (first version published on 7 December 2023) that implements both the ridge estimator and generalized ridge estimator. The package is equipped with generalized cross-validation for the automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on the R package “glmnet”. Hence the generalized ridge estimator may be the most recommended estimator for sparse and high-dimensional models. We demonstrate the package using intracerebral hemorrhage data. Full article
(This article belongs to the Special Issue Research Topics Related to Skew-Symmetric Distributions)
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21 pages, 368 KiB  
Article
Statistical Inference of Normal Distribution Based on Several Divergence Measures: A Comparative Study
by Suad Alhihi, Maalee Almheidat, Ghassan Abufoudeh, Raed Abu Awwad, Samer Alokaily and Ayat Almomani
Symmetry 2024, 16(2), 212; https://doi.org/10.3390/sym16020212 - 9 Feb 2024
Viewed by 1034
Abstract
Statistical predictive analysis is a very useful tool for predicting future observations. Previous literature has addressed both Bayesian and non-Bayesian predictive distributions of future statistics based on past sufficient statistics. This study focused on evaluating Bayesian and Wald predictive-density functions of a future [...] Read more.
Statistical predictive analysis is a very useful tool for predicting future observations. Previous literature has addressed both Bayesian and non-Bayesian predictive distributions of future statistics based on past sufficient statistics. This study focused on evaluating Bayesian and Wald predictive-density functions of a future statistic V based on a past sufficient statistic W obtained from a normal distribution. Several divergence measures were used to assess the closeness of the predictive densities to the future density. The difference between these divergence measures was investigated, using a simulation study. A comparison between the two predictive densities was examined, based on the power of a test. The application of a real data set was used to illustrate the results in this article. Full article
(This article belongs to the Special Issue Research Topics Related to Skew-Symmetric Distributions)
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11 pages, 543 KiB  
Article
Investigating the Lifetime Performance Index under Ishita Distribution Based on Progressive Type II Censored Data with Applications
by Hanan Haj Ahmad, Kariema Elnagar and Dina Ramadan
Symmetry 2023, 15(9), 1779; https://doi.org/10.3390/sym15091779 - 18 Sep 2023
Cited by 6 | Viewed by 1131
Abstract
In manufacturing sectors, product performance evaluation is crucial. The lifetime performance index, denoted as CL, is widely used in product evaluation, where L signifies the lower specification limit. This study aims to refine the estimation of CL by employing maximum-likelihood [...] Read more.
In manufacturing sectors, product performance evaluation is crucial. The lifetime performance index, denoted as CL, is widely used in product evaluation, where L signifies the lower specification limit. This study aims to refine the estimation of CL by employing maximum-likelihood and Bayesian methodologies, where symmetric and asymmetric loss functions are utilized. The analysis is conducted on progressive type II censored data, a requirement often imposed by budgetary constraints or the need for expedited testing. The data are assumed to follow the Ishita distribution, whose conforming rate is also evaluated. Furthermore, a hypothesis testing framework is employed to validate whether component lifetimes meet predefined standards. The theoretical findings are corroborated using real data collected from glass strength in aircraft windows. The numerical analysis emphasizes the goodness of fit of the Ishita distribution to model the data, thereby demonstrating the applicability of the proposed distribution. Full article
(This article belongs to the Special Issue Research Topics Related to Skew-Symmetric Distributions)
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19 pages, 2454 KiB  
Article
Statistical Modeling of Financial Data with Skew-Symmetric Error Distributions
by Masayuki Jimichi, Yoshinori Kawasaki, Daisuke Miyamoto, Chika Saka and Shuichi Nagata
Symmetry 2023, 15(9), 1772; https://doi.org/10.3390/sym15091772 - 15 Sep 2023
Cited by 4 | Viewed by 1716
Abstract
Based on corporate financial data for almost all companies listed on the Prime Market of the Tokyo Stock Exchange in fiscal year 2021, we gradually refine a model to explain firms’ sales by the number of employees and total assets. Starting from a [...] Read more.
Based on corporate financial data for almost all companies listed on the Prime Market of the Tokyo Stock Exchange in fiscal year 2021, we gradually refine a model to explain firms’ sales by the number of employees and total assets. Starting from a Cobb–Douglas-type functional form linearized by a log transformation, the assumption of a skew-symmetric distribution in the error structure and the introduction of industry dummies are shown to be useful not only in searching for a good-fitting model, but also in ensuring the accuracy of important parameters such as the labor share. The introduction of industry dummies helps to improve the accuracy of the model as well as to allow for interpretation as sector-wise total factor productivity. Full article
(This article belongs to the Special Issue Research Topics Related to Skew-Symmetric Distributions)
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18 pages, 900 KiB  
Article
On a Measure of Tail Asymmetry for the Bivariate Skew-Normal Copula
by Toshinao Yoshiba, Takaaki Koike and Shogo Kato
Symmetry 2023, 15(7), 1410; https://doi.org/10.3390/sym15071410 - 13 Jul 2023
Cited by 1 | Viewed by 1401
Abstract
Asymmetry in the upper and lower tails is an important feature in modeling bivariate distributions. This article focuses on the log ratio between the tail probabilities at upper and lower corners as a measure of tail asymmetry. Asymptotic behavior of this measure at [...] Read more.
Asymmetry in the upper and lower tails is an important feature in modeling bivariate distributions. This article focuses on the log ratio between the tail probabilities at upper and lower corners as a measure of tail asymmetry. Asymptotic behavior of this measure at extremely large and small thresholds is explored with particular emphasis on the skew-normal copula. Our numerical studies reveal that, when the correlation or skewness parameters are around at the boundary values, some asymptotic tail approximations of the skew-normal copulas proposed in the literature are not suitable to compute the measure of tail asymmetry with practically extremal thresholds. Full article
(This article belongs to the Special Issue Research Topics Related to Skew-Symmetric Distributions)
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