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Symmetry
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Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II
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Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II

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

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 16498

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

E-Mail Website
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

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 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:

I. 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.

II. Skewed distributions in describing natural processes.

  • 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;
  • Origin and fundamental interpretations of skewed distributions in mathematics, physics, chemistry, biology, and social sciences.

Submit your paper and select the Journal “Symmetry” and the Special Issue “Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Dr. Juan Carlos Castro-Palacio
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 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.

Published Papers (10 papers)

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Research

26 pages, 652 KiB  
Article
Statistical Inference for the Kavya–Manoharan Kumaraswamy Model under Ranked Set Sampling with Applications
by Naif Alotaibi, Ibrahim Elbatal, Mansour Shrahili, A. S. Al-Moisheer, Mohammed Elgarhy and Ehab M. Almetwally
Symmetry 2023, 15(3), 587; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15030587 - 24 Feb 2023
Cited by 11 | Viewed by 1615
Abstract
In this article, we introduce a new extension of the Kumaraswamy (Ku) model, which is called the Kavya Manoharan Kumaraswamy (KMKu) model. The shape forms of the pdf for the KMKu model for various values of parameters are similar to the Ku model. [...] Read more.
In this article, we introduce a new extension of the Kumaraswamy (Ku) model, which is called the Kavya Manoharan Kumaraswamy (KMKu) model. The shape forms of the pdf for the KMKu model for various values of parameters are similar to the Ku model. It can be asymmetric, such as bathtub, unimodal, increasing and decreasing. In addition, the shape forms of the hrf for the KMKu model can be bathtub, U-shaped, J-shaped and increasing. Several statistical and computational properties were computed. Four different measures of entropy were studied. The maximum likelihood approach was employed to estimate the parameters for the KMKu model under simple and ranked set sampling. A simulation experiment was conducted in order to calculate the model parameters of the KMKu model utilizing simple and ranked set sampling and show the efficiency of the ranked set sampling more than the simple random sampling. The KMKu has more flexibility than the Ku model and other well-known models, and we proved this using three real-world data sets. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)
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24 pages, 784 KiB  
Article
Confidence Interval Estimation for the Common Mean of Several Zero-Inflated Gamma Distributions
by Theerapong Kaewprasert, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2023, 15(1), 67; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15010067 - 26 Dec 2022
Cited by 1 | Viewed by 1343
Abstract
In this study, we propose estimates for the confidence interval for the common mean of several zero-inflated gamma (ZIG) distributions based on the fiducial generalized confidence interval (GCI) and Bayesian and highest posterior density (HPD) methods based on the Jeffreys rule or uniform [...] Read more.
In this study, we propose estimates for the confidence interval for the common mean of several zero-inflated gamma (ZIG) distributions based on the fiducial generalized confidence interval (GCI) and Bayesian and highest posterior density (HPD) methods based on the Jeffreys rule or uniform prior. Their performances in terms of their coverage probabilities and expected lengths are compared via a Monte Carlo simulation study. For almost all of the scenarios considered, the simulation results show that the fiducial GCI performed better than the Bayesian and HPD methods. Daily rainfall data from Chiang Mai Province, Thailand that contains several zero entries and follows a ZIG distribution is used to test the efficacies of the methods in real-world situations. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)
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15 pages, 495 KiB  
Article
Estimation of the Confidence Interval for the Ratio of the Coefficients of Variation of Two Weibull Distributions and Its Application to Wind Speed Data
by Manussaya La-ongkaew, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2023, 15(1), 46; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15010046 - 24 Dec 2022
Cited by 2 | Viewed by 1096
Abstract
The Weibull distribution, one of the most significant distributions with applications in numerous fields, is associated with numerous distributions such as generalized gamma distribution, exponential distribution, and Rayleigh distribution, which are asymmetric. Nevertheless, it shares a close relationship with a normal distribution where [...] Read more.
The Weibull distribution, one of the most significant distributions with applications in numerous fields, is associated with numerous distributions such as generalized gamma distribution, exponential distribution, and Rayleigh distribution, which are asymmetric. Nevertheless, it shares a close relationship with a normal distribution where a process of transformation allows them to become symmetric. The Weibull distribution is commonly used to study the failure of components and phenomena. It has been applied to a variety of scenarios, including failure time, claims amount, unemployment duration, survival time, and especially wind speed data. A suitable area for installing a wind turbine requires a wind speed that is both sufficiently high and consistent, and so comparing the variation in wind speed in two areas is eminently desirable. In this paper, methods to estimate the confidence interval for the ratio of the coefficients of variation of two Weibull distributions are proposed and applied to compare the variation in wind speed in two areas. The methods are the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER), and Bayesian methods based on the gamma and uniform priors. The Bayesian methods comprise the equal-tailed confidence interval and the highest posterior density (HPD) interval. The effectiveness of the methods was evaluated in terms of their coverage probabilities and expected lengths and also empirically applied to wind speed datasets from two different areas in Thailand. The results indicate that the HPD interval based on the uniform prior outperformed the others in most of the scenarios tested and so it is suggested for estimating the confidence interval for the ratio of the coefficients of variation of two Weibull distributions. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)
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17 pages, 1732 KiB  
Article
Simultaneous Confidence Intervals for All Pairwise Differences between the Coefficients of Variation of Multiple Birnbaum–Saunders Distributions
by Wisunee Puggard, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2022, 14(12), 2666; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14122666 - 16 Dec 2022
Cited by 1 | Viewed by 961
Abstract
In situations where several positive random variables cannot be described using symmetrical distributions, a positively asymmetric distribution which has garnered much attention for studying them is the Birnbaum-Saunders (BS) distribution. This distribution was originally proposed to study fatigue over time in materials and [...] Read more.
In situations where several positive random variables cannot be described using symmetrical distributions, a positively asymmetric distribution which has garnered much attention for studying them is the Birnbaum-Saunders (BS) distribution. This distribution was originally proposed to study fatigue over time in materials and has become widely employed for reliability and fatigue studies. In statistics, the coefficient of variation (CV) is employed to measure relative variation. Furthermore, comparing the CVs of several samples from BS distributions is an important approach to assess the variation among them. Herein, we propose estimation methods for the simultaneous confidence intervals (SCIs) for all pairwise differences between the CVs of multiple BS distributions based on the percentile bootstrap, the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER) based on the asymptotic confidence interval (ACI) and GCI, Bayesian credible interval, and the highest posterior density (HPD) interval. The coverage probabilities and average lengths of the proposed methods were examined via a simulation study to determine their performance. The results demonstrate that GCI and the MOVER based on the GCI method provided satisfactory performances in almost every case studied. Particulate matter ≤ 2.5 μm (PM2.5) concentration datasets from three areas in northern Thailand were used to illustrate the effectiveness of the proposed methods. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)
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7 pages, 424 KiB  
Article
Interval Estimation for the Two-Parameter Exponential Distribution Based on the Upper Record Values
by Shu-Fei Wu
Symmetry 2022, 14(9), 1906; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14091906 - 12 Sep 2022
Cited by 2 | Viewed by 1257
Abstract
Using the data for upper record values, the interval estimation for the scale parameter of two-parameter exponential distribution is presented. In addition, two methods for the joint confidence region of two parameters are proposed. In terms of confidence region area, the simulation comparison [...] Read more.
Using the data for upper record values, the interval estimation for the scale parameter of two-parameter exponential distribution is presented. In addition, two methods for the joint confidence region of two parameters are proposed. In terms of confidence region area, the simulation comparison of two methods of the confidence region is performed in this paper. The criterion of minimum confidence region area is used to obtain the optimal method of the confidence region. To illustrate our proposed interval estimation methods, one biometrical example is used and the corresponding confidence interval length and confidence region area are also calculated. Our research topic is related to the asymmetrical probability distributions and applications across disciplines. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)
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12 pages, 436 KiB  
Article
Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions
by Wisunee Puggard, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2022, 14(7), 1492; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14071492 - 21 Jul 2022
Cited by 2 | Viewed by 1246
Abstract
Fatigue in a material occurs when it is subjected to fluctuating stress and strain, which usually results in failure due to the accumulated damage. In statistics, asymmetric distribution, which is commonly used for describing the fatigue life of materials, is the Birnbaum–Saunders (BS) [...] Read more.
Fatigue in a material occurs when it is subjected to fluctuating stress and strain, which usually results in failure due to the accumulated damage. In statistics, asymmetric distribution, which is commonly used for describing the fatigue life of materials, is the Birnbaum–Saunders (BS) distribution. This distribution can be transform to the normal distribution, which is symmetrical. Furthermore, variance is used to examine the dispersion of the fatigue life data. However, comparing the variances of two independent samples that follow BS distributions has not previously been reported. To accomplish this, we propose methods for providing the confidence interval for the ratio of variances of two independent BS distributions based on the generalized fiducial confidence interval (GFCI), a Bayesian credible interval (BCI), and the highest posterior density (HPD) intervals based on a prior distribution with partial information (HPD-PI) and a proper prior with known hyperparameters (HPD-KH). A Monte Carlo simulation study was carried out to examine the efficacies of the methods in terms of their coverage probabilities and average lengths. The simulation results indicate that the HPD-PI performed satisfactorily for all sample sizes investigated. To illustrate the efficacies of the proposed methods with real data, they were also applied to study the confidence interval for the ratio of the variances of two 6061-T6 aluminum coupon fatigue-life datasets. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)
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14 pages, 4040 KiB  
Article
Cornish–Fisher-Based Control Charts Inclusive of Skewness and Kurtosis Measures for Monitoring the Mean of a Process
by Paul Braden and Timothy Matis
Symmetry 2022, 14(6), 1176; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14061176 - 07 Jun 2022
Viewed by 1290
Abstract
In this paper, we propose control limits for monitoring the mean of a process variable based on a first and second order Cornish–Fisher expansion, which limits are inclusive of its skewness and kurtosis measures, respectively. These are shown to have better in-control error [...] Read more.
In this paper, we propose control limits for monitoring the mean of a process variable based on a first and second order Cornish–Fisher expansion, which limits are inclusive of its skewness and kurtosis measures, respectively. These are shown to have better in-control error performance than other limits that were similarly derived from this expansion with smoothing functions, both when these measures are assumed to be known and estimated from sample data. The range of measure specifications where the underlying Cornish–Fisher function is monotonic is derived. Operating characteristic curves for select cases demonstrate the associated out-of-control error performance. The Cornish–Fisher limits are applied to a real-life dataset in developing a control chart for monitoring the mean lifetime of car brake pads, wherein they are compared to other limit approximations. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)
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15 pages, 383 KiB  
Article
Confidence Interval, Prediction Interval and Tolerance Interval for the Skew Normal Distribution: A Pivotal Approach
by Xinlei Qi, Huihui Li, Weizhong Tian and Yaoting Yang
Symmetry 2022, 14(5), 855; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14050855 - 21 Apr 2022
Cited by 4 | Viewed by 1951
Abstract
The class of skew normal distributions, introduced by Azzalini (1985), which is an asymmetric distribution and allows the presence of skewness. In this paper, we propose the pivotal quantity approach to construct the confidence interval for the mean, prediction interval for the mean [...] Read more.
The class of skew normal distributions, introduced by Azzalini (1985), which is an asymmetric distribution and allows the presence of skewness. In this paper, we propose the pivotal quantity approach to construct the confidence interval for the mean, prediction interval for the mean of the future sample, and tolerance interval for the quantile. The fiducial distribution is also studied. Moreover, the performances of all the proposed confidence intervals are investigated through the Monte Carlo simulation. The pivotal quantity is a common method for calculating confidence intervals, which is used to construct confidence intervals in this paper. And the convergence of the obtained confidence interval is illustrated by the figures. Finally, a real data is used to explain proposed intervals in real life. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)
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13 pages, 938 KiB  
Article
Asymmetric Laplace Distribution Models for Financial Data: VaR and CVaR
by Huiting Jing, Yang Liu and Jinghua Zhao
Symmetry 2022, 14(4), 807; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14040807 - 13 Apr 2022
Cited by 3 | Viewed by 2377
Abstract
In the field of financial risk measurement, Asymmetric Laplace (AL) laws are used. The assumption of normalcy is used in traditional approaches for calculating financial risk. Asymmetric Laplace distribution, on the other hand, reveals the properties of empirical financial data sets much better [...] Read more.
In the field of financial risk measurement, Asymmetric Laplace (AL) laws are used. The assumption of normalcy is used in traditional approaches for calculating financial risk. Asymmetric Laplace distribution, on the other hand, reveals the properties of empirical financial data sets much better than the normal model by leptokurtosis and skewness. According to recent financial data research, the regularity assumption is frequently broken. As a result, Asymmetric Laplace laws offer a simple, creative, and useful option to normal distributions when it comes to modeling financial data. We here engage AL distribution to explore specific formulas for the two commonly used risk measures, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). The currency exchange rates data are used to and worked out to illustrate the proposed methodologies. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)
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10 pages, 855 KiB  
Article
Bayesian Interval Estimation for the Two-Parameter Exponential Distribution Based on the Right Type II Censored Sample
by Shu-Fei Wu
Symmetry 2022, 14(2), 352; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14020352 - 10 Feb 2022
Cited by 5 | Viewed by 1844
Abstract
The Bayesian interval estimation of the scale parameter for two-parameter exponential distribution is proposed based on the right type II censored sample. Under this type of censoring, two methods of Bayesian joint confidence region of the two parameters are also proposed. The simulation [...] Read more.
The Bayesian interval estimation of the scale parameter for two-parameter exponential distribution is proposed based on the right type II censored sample. Under this type of censoring, two methods of Bayesian joint confidence region of the two parameters are also proposed. The simulation results show that the Bayesian method has a higher coverage probability than the existing method, so the Bayesian method is recommended for use. This research is related to the topic of asymmetrical probability distributions and applications across disciplines. The predictive interval of the future observation based on the right type II censored sample is also provided. One biometrical example is given to illustrate the proposed methods for the Bayesian interval estimations and prediction interval. Full article
(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines II)
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