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Symmetry
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Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines, 5th Edition
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Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines, 5th Edition

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

Deadline for manuscript submissions: 31 August 2026 | Viewed by 1189

Special Issue Editors

Prof. Dr. Pedro José Fernández de Córdoba Castellá

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

E-Mail Website
Guest Editor
Department of Statistics, Tamkang University, Taipei 251301, Taiwan
Interests: statistics
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 having a deep understanding of their underlying probabilistic mechanisms is crucial in many fields. Identifying the correct probability distribution for a non-normal stochastic process and the proper interpretation of its parameters can be very challenging, though doing so is of enormous importance in fields such as physics, chemistry, biology, and social sciences.

Contributions to this Special Issue can cover 0(but are not limited to) the following topics, which are divided into two broad groups:

  • Methods and applications of skew distribution:
    • 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.

Prof. Dr. Pedro José Fernández de Córdoba Castellá
Prof. Dr. Shufei Wu
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 250 words) can be sent to the Editorial Office for assessment.

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

  • skewed distributions
  • non-normal distributions
  • parameter estimation
  • statistical modelling
  • stochastic processes
  • numerical methods

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Related Special Issue

Published Papers (3 papers)

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Research

29 pages, 1864 KB  
Article
Confidence Intervals for Parameter Variance of Zero-Inflated Two-Parameter Rayleigh Distribution
by Sasipong Kijsason, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2026, 18(5), 765; https://doi.org/10.3390/sym18050765 - 29 Apr 2026
Viewed by 197
Abstract
This study develops confidence and credible intervals for the variance of the zero-inflated two-parameter Rayleigh distribution, a flexible model for non-negative data with excess zeros. Seven approaches are proposed: Bayesian Markov chain Monte Carlo (MCMC), Bayesian highest posterior density (HPD), the standard confidence [...] Read more.
This study develops confidence and credible intervals for the variance of the zero-inflated two-parameter Rayleigh distribution, a flexible model for non-negative data with excess zeros. Seven approaches are proposed: Bayesian Markov chain Monte Carlo (MCMC), Bayesian highest posterior density (HPD), the standard confidence interval, the approximation normal, the percentile bootstrap, the bootstrap method with standard error, and the generalized confidence interval (GCI). Their performance is assessed through Monte Carlo simulation using coverage probability (CP) and expected length (EL). The results show that the Bayesian HPD interval performs best overall, attaining coverage close to the nominal level while yielding shorter intervals than the alternatives, especially for small samples. The methods are illustrated with road traffic fatality data from Chiang Mai Province, Thailand, recorded in March 2024. These findings support the practical usefulness of the HPD approach for variance interval estimation in zero-inflated continuous models. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines, 5th Edition)
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18 pages, 355 KB  
Article
Shewhart-Type TBEA Charts for Monitoring Frequency and Amplitude with Symmetry Structure Under Generalized Weibull and Generalized Log-Logistic Distributions
by Mustafa M. Hasaballah, Arvind Pandey, Pragya Gupta, Oluwafemi Samson Balogun, Farouq Mohammad A. Alam and Mahmoud E. Bakr
Symmetry 2026, 18(5), 750; https://doi.org/10.3390/sym18050750 (registering DOI) - 27 Apr 2026
Viewed by 215
Abstract
Control charts for monitoring time between events (T) and amplitude (X) have been developed in recent years. Many TBEA charts depend on limited models such as exponential, normal, and gamma distributions and mainly rely on the ratio statistic ( [...] Read more.
Control charts for monitoring time between events (T) and amplitude (X) have been developed in recent years. Many TBEA charts depend on limited models such as exponential, normal, and gamma distributions and mainly rely on the ratio statistic (XT). This representation ignores the symmetric relationship between event occurrence and event magnitude. This paper proposes Shewhart-type TBEA charts constructed from three statistics (Z1), (Z2), and (Z3) based on (X) and (T). The approach models symmetry between frequency and amplitude using generalized Weibull and generalized log-logistic distributions. The statistics maintain proportional invariance when both variables shift together, which enables balanced monitoring of the process. Several scenarios are examined for detecting upward shifts. Performance is assessed using numerical measures of detection efficiency and average run length. The results show improved detection compared with classical ratio-based TBEA charts. A real data example from a French forest fire database illustrates the ability of the proposed charts to detect simultaneous changes in occurrence rate and burn intensity. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines, 5th Edition)
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25 pages, 2055 KB  
Article
Simultaneous Confidence Intervals for All Pairwise Differences of Coefficients of Variation of Delta-Inverse Gaussian Distributions
by Wasurat Khumpasee, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2026, 18(4), 604; https://doi.org/10.3390/sym18040604 - 2 Apr 2026
Viewed by 365
Abstract
This study develops and evaluates simultaneous confidence interval procedures for all pairwise differences of coefficients of variation under delta-inverse Gaussian distributions. The objective is to provide reliable comparative inference for relative variability in zero-inflated and highly skewed data, where standard normal-based methods may [...] Read more.
This study develops and evaluates simultaneous confidence interval procedures for all pairwise differences of coefficients of variation under delta-inverse Gaussian distributions. The objective is to provide reliable comparative inference for relative variability in zero-inflated and highly skewed data, where standard normal-based methods may be unreliable. Five approaches were studied and compared in terms of coverage probabilities and average widths: generalized confidence interval, adjusted generalized confidence interval, fiducial confidence interval, method of variance estimates recovery, and normal approximation. A Monte Carlo simulation study was conducted under varying shape parameters, zero-inflation probabilities, sample sizes, and numbers of populations (k = 3, 6, and 10). Although most methods produced CPs near the nominal 0.95 level, meaningful differences emerged when both coverage accuracy and interval efficiency were considered. The AGCI method consistently delivered stable coverage across parameter settings and remained robust as dimensionality increased. The MOVER approach achieved competitive coverage while frequently yielding narrower intervals. In contrast, GCI occasionally showed mild undercoverage, and FCI tended to produce overly wide intervals. An empirical application to zero-inflated mortality data supports the simulation findings. Overall, AGCI and MOVER provide reliable and practical tools for simultaneous inference on differences in CVs across delta-IG populations. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines, 5th Edition)
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