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Symmetry
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Symmetric and Asymmetric Distributions: New Developments and Applications
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Symmetric and Asymmetric Distributions: New Developments and Applications

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

Deadline for manuscript submissions: 31 July 2025 | Viewed by 9643

Special Issue Editors

Prof. Dr. Emilio Gómez Déniz

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Guest Editor
Department of Quantitative Methods and TIDES Institute, University of Las Palmas de Gran Canaria, Campus de Tafira s/n, 35017 Las Palmas, Spain
Interests: distributions theory; Bayesian statistics; robustness; Bayesian applications in economics (actuarial, credibility, ruin theory)
Special Issues, Collections and Topics in MDPI journals
Dr. Enrique Calderín-Ojeda

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Guest Editor
Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Melbourne, Australia
Interests: actuarial statistics; bayesian statistics; distribution theory
Special Issues, Collections and Topics in MDPI journals
Dr. Héctor W. Gómez

E-Mail Website
Guest Editor
Departamento de Estadística y Ciencias de Datos, Universidad de Antofagasta, Antofagasta, Chile
Interests: distribution theory; classical and Bayesian inferencia; actuarial statistical; regression
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is intended as a natural extension of the previous Special Issues, entitled “Symmetric and Asymmetric Distributions: Theoretical Developments and Applications”, “Symmetric and Asymmetric Distributions: Theoretical Developments and Applications II”, and “Symmetric and Asymmetric Distributions: Theoretical Developments and Applications III”. In launching this Special Issue is the success achieved by the previous issues, which has contributed to increasing the catalogue of continuous and discrete, univariate and multivariate, distributions available in the statistical literature.

We would like to invite researchers in the statistical field to submit papers related to symmetric and asymmetric distributions. Undoubtedly, their field of application is extensive, covering disciplines in areas as diverse as the social sciences, medicine, applied physics, and a whole host of others. In turn, for each of these areas, the field of application is diverse, interdisciplinary, and multidisciplinary, allowing authors to modelling scenarios from areas as diverse as finance, economics, health economics, actuarial statistics, survival analysis, reliability, environmental sciences, climate change, sustainability, and many more besides.

Currently, the improvement of computational tools makes it possible to manage databases that just several decades prior were prohibitive, also allowing the use of special functions that, without computer processing, it would be impossible to implement in statistical models.

We encourage all researchers working in these areas and other fields to submit papers to be evaluated anonymously and possibly published in this prestigious and widely disseminated journal with wide dissemination in the field of statistics. In particularly, we are seeking to publih theoretical and practical contributions in which the use of probability distributions is fundamental and has demonstrated its usefulness as an unquestionable predictive tool.

Prof. Dr. Emilio Gómez Déniz
Dr. Enrique Calderín-Ojeda
Dr. Héctor W. Gómez
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

  • applications
  • Bayesian
  • regression
  • reliability
  • simulation
  • skewness
  • survival analysis

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

Published Papers (6 papers)

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Research

20 pages, 452 KiB  
Article
Estimation of P(X < Y) Stress–Strength Reliability Measures for a Class of Asymmetric Distributions: The Case of Three-Parameter p-Max Stable Laws
by Felipe Sousa Quintino, Pushpa Narayan Rathie, Luan Carlos de Sena Monteiro Ozelim and Tiago Alves da Fonseca
Symmetry 2024, 16(7), 837; https://doi.org/10.3390/sym16070837 - 3 Jul 2024
Cited by 3 | Viewed by 1315
Abstract
Asymmetric distributions are frequently seen in real-world datasets due to a number of factors, such as sample biases and nonlinear interactions between the variables observed. Thus, in order to better characterize real-world phenomena, studying asymmetric distribution is of great interest. In this work, [...] Read more.
Asymmetric distributions are frequently seen in real-world datasets due to a number of factors, such as sample biases and nonlinear interactions between the variables observed. Thus, in order to better characterize real-world phenomena, studying asymmetric distribution is of great interest. In this work, we derive stress–strength reliability formulas of the type P(X<Y) when both X and Y follow p-max stable laws with three parameters, which are inherently asymmetric. The new relations are given in terms of extreme-value H-functions and have been obtained under fewer parameter restrictions when compared to similar results in the literature. We estimate the parameters of the p-max stable laws by a stochastic optimization method and the stress–strength probability by a maximum likelihood procedure. The performance of the analytical models is evaluated through simulations and real-life dataset modeling. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Distributions: New Developments and Applications)
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28 pages, 39687 KiB  
Article
Reliability Analysis and Its Applications for a Newly Improved Type-II Adaptive Progressive Alpha Power Exponential Censored Sample
by Ibrahim Elbatal, Mazen Nassar, Anis Ben Ghorbal, Lamiaa Sabry Gad Diab and Ahmed Elshahhat
Symmetry 2023, 15(12), 2137; https://doi.org/10.3390/sym15122137 - 1 Dec 2023
Cited by 9 | Viewed by 1335
Abstract
Recently, a newly improved Type-II adaptive progressive censoring plan was devised, which can successfully ensure that the test length will not surpass a particular threshold period. In this study, we explore the statistical inference of the alpha power exponential distribution in the context [...] Read more.
Recently, a newly improved Type-II adaptive progressive censoring plan was devised, which can successfully ensure that the test length will not surpass a particular threshold period. In this study, we explore the statistical inference of the alpha power exponential distribution in the context of improved adaptive progressive Type-II censored data. The parameters, reliability, and hazard functions were estimated from both classical and Bayesian viewpoints using this censoring plan. To begin, we applied the maximum likelihood estimation approach to obtain parameter, reliability, and hazard function estimators. Following that, the approximate confidence intervals for the aforementioned metrics were derived, assuming the asymptotic normality traits of the maximum likelihood estimators. Additionally, by employing the Bayesian method via the Markov chain Monte Carlo technique, the point estimators and highest posterior density intervals of various parameters were created based on the symmetric squared error loss. A simulation study that incorporates numerous scenarios was used to assess the effectiveness of various estimation methodologies. The optimal progressive censorship plans are then discussed based on a set of criteria. Finally, three applications from the engineering and medical domains have been offered as examples. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Distributions: New Developments and Applications)
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21 pages, 914 KiB  
Article
A Novel Probabilistic Approach Based on Trigonometric Function: Model, Theory with Practical Applications
by Omalsad Hamood Odhah, Huda M. Alshanbari, Zubair Ahmad, Faridoon Khan and Abd Al-Aziz Hosni El-Bagoury
Symmetry 2023, 15(8), 1528; https://doi.org/10.3390/sym15081528 - 2 Aug 2023
Cited by 26 | Viewed by 1467
Abstract
Proposing new families of probability models for data modeling in applied sectors is a prominent research topic. This paper also proposes a new method based on the trigonometric function to derive the updated form of the existing probability models. The proposed family is [...] Read more.
Proposing new families of probability models for data modeling in applied sectors is a prominent research topic. This paper also proposes a new method based on the trigonometric function to derive the updated form of the existing probability models. The proposed family is called the cotangent trigonometric-G family of distributions. Based on the cotangent trigonometric-G method, a new version of the Weibull model, namely, the cotangent trigonometric Weibull distribution, is studied. Certain mathematical properties of the cotangent trigonometric-G family are derived. The estimators of the cotangent trigonometric-G distributions are obtained via the maximum likelihood method. The Monte Carlo simulation study is conducted to assess the performances of the estimators. Finally, two applications from the health sector are considered to illustrate the cotangent trigonometric-G method. Based on seven evaluating criteria, it is observed that the cotangent trigonometric-G significantly improves the fitting power of the existing models. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Distributions: New Developments and Applications)
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27 pages, 9054 KiB  
Article
A New Xgamma–Weibull Model Using Type-II Adaptive Progressive Hybrid Censoring and Its Applications in Engineering and Medicine
by Heba S. Mohammed, Mazen Nassar and Ahmed Elshahhat
Symmetry 2023, 15(7), 1428; https://doi.org/10.3390/sym15071428 - 16 Jul 2023
Cited by 1 | Viewed by 1278
Abstract
This paper is an attempt to study the Xgamma–Weibull distribution using an adaptive progressive type-II censoring plan. This scheme effectively ensures that the experimental time does not exceed a predetermined time limit. Using two classical estimation methods—namely, maximum likelihood and maximum product of [...] Read more.
This paper is an attempt to study the Xgamma–Weibull distribution using an adaptive progressive type-II censoring plan. This scheme effectively ensures that the experimental time does not exceed a predetermined time limit. Using two classical estimation methods—namely, maximum likelihood and maximum product of spacing—both point and interval estimations for the unknown model parameters, as well as some parameters of life—namely, reliability and hazard rate functions—were obtained. The asymptotic normality of both classical methods was used to determine the approximate confidence intervals for the various parameters. Based on the two conventional methodologies, Bayesian estimations were also investigated using the MCMC technique under the squared error loss function. In addition, the credible intervals of the different parameters were also obtained. To compare the performance of the various approaches, a thorough simulation study was carried out. Furthermore, we propose using several optimality criteria to select the best sampling technique. Finally, two real-world datasets were used to demonstrate how the suggested estimators and optimality criteria operate in real-world circumstances. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Distributions: New Developments and Applications)
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13 pages, 372 KiB  
Article
Robust Semi-Parametric Inference for Two-Stage Production Models: A Beta Regression Approach
by Raydonal Ospina, Samuel G. F. Baltazar, Víctor Leiva, Jorge Figueroa-Zúñiga and Cecilia Castro
Symmetry 2023, 15(7), 1362; https://doi.org/10.3390/sym15071362 - 4 Jul 2023
Viewed by 1467
Abstract
The data envelopment analysis is related to a non-parametric mathematical tool used to assess the relative efficiency of productive units. In different studies on productive efficiency, it is common to employ semi-parametric procedures in two stages to determine whether any exogenous factors of [...] Read more.
The data envelopment analysis is related to a non-parametric mathematical tool used to assess the relative efficiency of productive units. In different studies on productive efficiency, it is common to employ semi-parametric procedures in two stages to determine whether any exogenous factors of interest affect the performance of productive units. However, some of these procedures, particularly those based on conventional statistical inference, generate inconsistent estimates when dealing with incoherent data-generating processes. This inconsistency arises due to the efficiency scores being limited to the unit interval, and the estimated scores often exhibit serial correlation and have limited observations. To address such inconsistency, several strategies have been suggested, with the most well-known being an algorithm based on a parametric bootstrap procedure using the truncated normal distribution and its regression model. In this work, we present a modification of this algorithm that utilizes the beta distribution and its regression structure. The beta model allows for better accommodation of asymmetry in the data distribution. Our proposed algorithm introduces inferential characteristics that are superior to the original algorithm, resulting in a more statistically coherent data-generating process and improving the consistency property. We have conducted computational experiments that demonstrate the improved results achieved by our proposal. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Distributions: New Developments and Applications)
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25 pages, 3225 KiB  
Article
The Discrete Exponentiated-Chen Model and Its Applications
by Refah Alotaibi, Hoda Rezk, Chanseok Park and Ahmed Elshahhat
Symmetry 2023, 15(6), 1278; https://doi.org/10.3390/sym15061278 - 18 Jun 2023
Cited by 5 | Viewed by 1987
Abstract
A novel discrete exponentiated Chen (DEC) distribution, which is a subset of the continuous exponentiated Chen distribution, is proposed. The offered model is more adaptable to analyzing a wide range of data than traditional and recently published models. Several important statistical and reliability [...] Read more.
A novel discrete exponentiated Chen (DEC) distribution, which is a subset of the continuous exponentiated Chen distribution, is proposed. The offered model is more adaptable to analyzing a wide range of data than traditional and recently published models. Several important statistical and reliability characteristics of the DEC model are introduced. In the presence of Type-II censored data, the maximum likelihood and asymptotic confidence interval estimators of the model parameters are acquired. Two various bootstrapping estimators of the DEC parameters are also obtained. To examine the efficacy of the adopted methods, several simulations are implemented. To further clarify the offered model in the life scenario, the two applications, based on the number of vehicle fatalities in South Carolina in 2012 and the final exam marks in 2004 at the Indian Institute of Technology at Kanpur, are analyzed. The analysis findings showed that the DEC model is the most effective model for fitting the supplied data sets compared to eleven well-known models in literature, including: Poisson, geometric, negative binomial, discrete-Weibull, discrete Burr Type XII, discrete generalized exponential, discrete-gamma, discrete Burr Hatke, discrete Nadarajah-Haghighi, discrete modified-Weibull, and exponentiated discrete-Weibull models. Ultimately, the new model is recommended to be applied in many fields of real practice. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Distributions: New Developments and Applications)
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