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Symmetry
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Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines Fourth Edition
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Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines Fourth Edition

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

Deadline for manuscript submissions: 31 March 2025 | Viewed by 5086

Special Issue Editors

Dr. Juan Carlos Castro-Palacio

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Guest Editor
Centro de Tecnologías Físicas, Universitat Politècnica de València, 46022 Valencia, Spain
Interests: physics teaching; atomistic dynamics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Pedro José Fernández de Córdoba Castellá

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Guest Editor
Grupo de Modelización Interdisciplinar, InterTech, Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera, 46022 Valencia, Spain
Interests: mathematical modeling; numerical simulation
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Shufei Wu

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Guest Editor
Department of Statistics, Tamkang University, Taipei 251301, Taiwan
Interests: statistics
Special Issues, Collections and Topics in MDPI journals
Dr. Miguel Enrique Iglesias Martínez

E-Mail Website
Guest Editor
1. Grupo de Modelización Interdisciplinar, InterTech, Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera, 46022 Valencia, Spain
2. Grupo de Ingeniería Física, Escuela de Ingeniería Aeronáutica y del Espacio, Universidad de Vigo, Edif. Manuel Martínez Risco, Campus de As Lagoas, 32004 Ourense, Spain
Interests: statistical signal processing; automated pattern recognition; electronics and communication
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Skewed distributions are transversal and ubiquitous to all scientific disciplines. They have captured the attention of many researchers, as a deep understanding of their underlying probabilistic mechanisms is crucial in many fields. The right choice of the probability distribution for a non-normal stochastic process and the proper interpretation of its parameters can be very challenging and of enormous importance in fields such as physics, chemistry, biology, and social sciences.

The guidelines for contributions to this Special Issue include (but are not limited to) the following topics, which are divided into two broad groups:

  • Methods and applications of skew distributions.
    • New applications and parameter interpretations of the main skewed distributions;
    • Parameter estimation and statistical developments;
    • Advances in modelling and simulations (i.e., Monte Carlo sampling) of processes in mathematics, physics, chemistry, biology, and social sciences;
    • Efficient numerical methods to handle skewed distributions;
    • Skewed distributions and the modelling of infectious diseases, including COVID-19.
  • Skewed distributions in describing natural processes.
    • The true meaning of skewed distributions in nature;
    • Skewed distributions in psychological and neurological sciences;
    • Non-normal distributions in biological and medical sciences;
    • Skewed distributions in describing social processes;
    • The origin and fundamental interpretations of skewed distributions in mathematics, physics, chemistry, biology, and social sciences.

Dr. Juan Carlos Castro-Palacio
Prof. Dr. Pedro José Fernández de Córdoba Castellá
Prof. Dr. Shufei Wu
Dr. Miguel Enrique Iglesias Martínez
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

  • new applications and parameter interpretations of the main skewed distributions
  • parameter estimation and statistical developments
  • advances in modelling and simulations (i.e., Monte Carlo sampling) of processes in mathematics, physics, chemistry, biology, and social sciences
  • efficient numerical methods to handle skewed distributions
  • skewed distributions and the modelling of infectious diseases, including COVID-19
  • the true meaning of skewed distributions in nature
  • skewed distributions in psychological and neurological sciences
  • non-normal distributions in biological and medical sciences
  • skewed distributions in describing social processes
  • the origin and fundamental interpretations of skewed distributions in mathematics, physics, chemistry, biology, and social sciences

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

Related Special Issue

Published Papers (6 papers)

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Research

22 pages, 3167 KiB  
Article
Gumbel–Logistic Unit Distribution with Application in Telecommunications Data Modeling
by Vladica S. Stojanović, Mihailo Jovanović, Brankica Pažun, Zlatko Langović and Željko Grujčić
Symmetry 2024, 16(11), 1513; https://doi.org/10.3390/sym16111513 - 11 Nov 2024
Viewed by 387
Abstract
The manuscript deals with a new unit distribution that depends on two positive parameters. The distribution itself was obtained from the Gumbel distribution, i.e., by its transformation, using generalized logistic mapping, into a unit interval. In this way, the so-called Gumbel-logistic unit (abbr. [...] Read more.
The manuscript deals with a new unit distribution that depends on two positive parameters. The distribution itself was obtained from the Gumbel distribution, i.e., by its transformation, using generalized logistic mapping, into a unit interval. In this way, the so-called Gumbel-logistic unit (abbr. GLU) distribution is obtained, and its key properties, such as cumulative distribution function, modality, hazard and quantile function, moment-based characteristics, Bayesian inferences and entropy, have been investigated in detail. Among others, it is shown that the GLU distribution, unlike the Gumbel one which is always positively asymmetric, can take both asymmetric forms. An estimation of the parameters of the GLU distribution, based on its quantiles, is also performed, together with asymptotic properties of the estimates thus obtained and their numerical simulation. Finally, the GLU distribution has been applied in modeling the empirical distributions of some real-world data related to telecommunications. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines Fourth Edition)
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13 pages, 1302 KiB  
Article
Confidence Intervals for the Coefficient of Variation in Delta Inverse Gaussian Distributions
by Wasurat Khumpasee, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2024, 16(11), 1488; https://doi.org/10.3390/sym16111488 - 7 Nov 2024
Viewed by 698
Abstract
The inverse Gaussian distribution is characterized by its asymmetry and right-skewed shape, indicating a longer tail on the right side. This distribution represents extreme values in one direction, such as waiting times, stochastic processes, and accident counts. Moreover, depending on if the accident [...] Read more.
The inverse Gaussian distribution is characterized by its asymmetry and right-skewed shape, indicating a longer tail on the right side. This distribution represents extreme values in one direction, such as waiting times, stochastic processes, and accident counts. Moreover, depending on if the accident counts data can occur or not and may have zero value, the Delta Inverse Gaussian (Delta-IG) distribution is more suitable. The confidence interval (CI) for the coefficient of variation (CV) of the Delta-IG distribution in accident counts is essential for risk assessment, resource allocation, and the creation of transportation safety policies. Our objective is to establish CIs of CV for the Delta-IG population using various methods. We considered seven CI construction methods, namely Generalized Confidence Interval (GCI), Adjusted Generalized Confidence Interval (AGCI), Parametric Bootstrap Percentile Confidence Interval (PBPCI), Fiducial Confidence Interval (FCI), Fiducial Highest Posterior Density Confidence Interval (F-HPDCI), Bayesian Credible Interval (BCI), and Bayesian Highest Posterior Density Credible Interval (B-HPDCI). We utilized Monte Carlo simulations to assess the proposed CI technique for average widths (AWs) and coverage probability (CP). Our findings revealed that F-HPDCI and AGCI exhibited the most effective coverage probability and average widths. We applied these methods to generate CIs of CV for accident counts in India. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines Fourth Edition)
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16 pages, 533 KiB  
Article
On a Randomly Censoring Scheme for Generalized Logistic Distribution with Applications
by Mustafa M. Hasaballah, Oluwafemi Samson Balogun and Mahmoud E. Bakr
Symmetry 2024, 16(9), 1240; https://doi.org/10.3390/sym16091240 - 21 Sep 2024
Viewed by 487
Abstract
In this paper, we investigate the inferential procedures within both classical and Bayesian frameworks for the generalized logistic distribution under a random censoring model. For randomly censored data, our main goals were to develop maximum likelihood estimators and construct confidence intervals using the [...] Read more.
In this paper, we investigate the inferential procedures within both classical and Bayesian frameworks for the generalized logistic distribution under a random censoring model. For randomly censored data, our main goals were to develop maximum likelihood estimators and construct confidence intervals using the Fisher information matrix for the unknown parameters. Additionally, we developed Bayes estimators with gamma priors, addressing both squared error and general entropy loss functions. We also calculated Bayesian credible intervals for the parameters. These methods were applied to two real datasets with random censoring to provide valuable insights. Finally, we conducted a simulation analysis to assess the effectiveness of the estimated values. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines Fourth Edition)
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18 pages, 526 KiB  
Article
A New Multimodal Modification of the Skew Family of Distributions: Properties and Applications to Medical and Environmental Data
by Jimmy Reyes, Mario A. Rojas, Pedro L. Cortés and Jaime Arrué
Symmetry 2024, 16(9), 1224; https://doi.org/10.3390/sym16091224 - 18 Sep 2024
Viewed by 906
Abstract
The skew distribution has the characteristic of appropriately modeling asymmetric unimodal data. However, in practice, there are several cases in which the data present more than one mode. In the literature, it is possible to find a large number of authors who have [...] Read more.
The skew distribution has the characteristic of appropriately modeling asymmetric unimodal data. However, in practice, there are several cases in which the data present more than one mode. In the literature, it is possible to find a large number of authors who have studied extensions based on the skew distribution to model this type of data. In this article, a new family is introduced, consisting of a multimodal modification to the family of skew distributions. Using the methodology of the weighted version of a function, we perform the product of the density function of a family of skew distributions with a polynomial of degree 4, thus obtaining a more flexible model that allows modeling data sets, whose distribution contains at most three modes. The density function, some properties, moments, skewness coefficients, and kurtosis of this new family are presented. This study focuses on the particular cases of skew-normal and Laplace distributions, although it can be applied to any other distribution. A simulation study was carried out, to study the behavior of the model parameter estimates. Illustrations with real data, referring to medicine and environmental data, show the practical performance of the proposed model in the two particular cases presented. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines Fourth Edition)
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11 pages, 1079 KiB  
Article
The Optimal Experimental Design for Exponentiated Frech’et Lifetime Products
by Shu-Fei Wu
Symmetry 2024, 16(9), 1132; https://doi.org/10.3390/sym16091132 - 2 Sep 2024
Viewed by 667
Abstract
In many manufacturing industries, the lifetime performance index CL is utilized to assess the manufacturing process performance for products following some lifetime distributions and subjecting them to progressive type I interval censoring. This paper aims to explore the sampling design required to [...] Read more.
In many manufacturing industries, the lifetime performance index CL is utilized to assess the manufacturing process performance for products following some lifetime distributions and subjecting them to progressive type I interval censoring. This paper aims to explore the sampling design required to achieve a specified level of significance and test power for products with lifetimes following the Exponentiated Frech’et distribution. Since lifetime distribution is an asymmetrical probability distribution, this investigation is related to the topic of asymmetrical probability distributions and applications in various fields. When the termination time is fixed but the number of intervals is variable, the optimal number of inspection intervals and sample sizes yielding the minimized total experimental costs are determined and tabulated. When the termination time is varying, the optimal number of inspection intervals, sample sizes, and equal interval lengths achieving the minimum total experimental costs are determined and tabulated. Optimal parameter values are displayed in tabular form for feasible applications for users. Additionally, a practical example is provided to illustrate how this sampling design can be used to collect data by using the optimal setup of parameters, followed by a testing procedure to assess the capability of the production process. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines Fourth Edition)
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20 pages, 484 KiB  
Article
Estimating the Confidence Interval for the Common Coefficient of Variation for Multiple Inverse Gaussian Distributions
by Wasana Chankham, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2024, 16(7), 886; https://doi.org/10.3390/sym16070886 - 11 Jul 2024
Viewed by 1043
Abstract
The inverse Gaussian distribution is a two-parameter continuous probability distribution with positive support, which is used to account for the asymmetry of the positively skewed data that are often seen when modeling environmental phenomena, such as PM2.5 levels. The coefficient of [...] Read more.
The inverse Gaussian distribution is a two-parameter continuous probability distribution with positive support, which is used to account for the asymmetry of the positively skewed data that are often seen when modeling environmental phenomena, such as PM2.5 levels. The coefficient of variation is often used to assess variability within datasets, and the common coefficient of variation of several independent samples can be used to draw inferences between them. Herein, we provide estimation methods for the confidence interval for the common coefficient of variation of multiple inverse Gaussian distributions by using the generalized confidence interval (GCI), the fiducial confidence interval (FCI), the adjusted method of variance estimates recovery (MOVER), and the Bayesian credible interval (BCI) and highest posterior density (HPD) methods using the Jeffreys prior rule. The estimation methods were evaluated based on their coverage probabilities and average lengths, using a Monte Carlo simulation study. The findings indicate the superiority of the GCI over the other methods for nearly all of the scenarios considered. This was confirmed for a real-world scenario involving PM2.5 data from three provinces in northeastern Thailand that followed inverse Gaussian distributions. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines Fourth Edition)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: A Simplified Discrete Model for Analyzing the Human Response Times to Visual Stimuli
Authors: Aina Noverques Medina; Marcos Orellana; José Guerra Carmenate; Miguel E. Iglesias Martínez; Juan Carlos Castro Palacio; Pedro Fernández de Córdoba.
Affiliation: Universitat Politècnica de València (UPV), Spain.
Abstract: In this paper, we streamline the model proposed in a previous study for representing the distribution of human response times to visual stimuli. We employ a Rayleigh distribution to depict the response time distribution within a group. Additionally, we introduce a discrete model to accurately compute the unique parameter B of the distribution. The obtained results quantitatively improve the previous work results considering the correlations values.

Title: Gumbel-Logistic Unit Distribution with Application in Telecommunications Data Modelling
Authors: Vladica S. Stojanović^1,a, Mihailo Jovanović^1,b, Brankica Pažun^2 and Zlatko Langović˘3
Affiliation: 1^Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, Belgrade, Serbia 2^Department of Informatics, Mathematics and Statistics, Faculty of Engineering Management, Belgrade, Serbia 3^Department of Business Economy, Faculty of Hotel Management and Tourism, University of Kragujevac, Vrnjačka Banja, Serbia
Abstract: The manuscript deals with a new two-parameter unit stochastic distribution, obtained by transforming the Gumbel distribution, using generalized logistic mapping, into a unit interval. The distribution obtained in this way is called the Gumbel-Logistic Unit (abbreviated GLU) distribution and its basic stochastic properties are examined in detail. Among others, it is shown that the GLU distribution, unlike the Gumbel one which is always positively asymmetric, can take both asymmetric forms. Also, the procedure for estimating parameters based on quantiles, along with the asymptotic properties of the obtained estimators and the study of their numerical simulation, is given. Finally, the application of the GLU distribution in modeling some real-world data related to telecommunications is discussed.

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