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Symmetry
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Symmetrical and Asymmetrical Distributions in Statistics and Data Science II
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Symmetrical and Asymmetrical Distributions in Statistics and Data Science II

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 7406

Special Issue Editors

Dr. Arne Johannssen

E-Mail Website
Guest Editor
Faculty of Business Administration, University of Hamburg, 20146 Hamburg, Germany
Interests: actuarial sciences; Artificial Intelligence; biostatistics; business analytics; computational statistics; data science; quantitative risk management; soft computing; statistical inference; statistical quality control
Special Issues, Collections and Topics in MDPI journals
Dr. Nataliya Chukhrova

E-Mail Website
Guest Editor
Faculty of Business Administration, University of Hamburg, 20146 Hamburg, Germany
Interests: Artificial Intelligence; biostatistics; business analytics; computational statistics; data science; fuzzy statistics; quantitative risk management; soft computing; statistical inference; statistical quality control
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Quanxin Zhu

grade E-Mail Website
Guest Editor
School of Mathematical Sciences and Statistics, Hunan Normal University, Changsha 410081, China
Interests: stochastic control; stochastic systems; stochastic stability; stochastic delayed systems; markovian jump systems; stochastic complex networks
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Due to the great success of our Special Issue "Symmetrical and Asymmetrical Distributions in Statistics and Data Science", we decided to set up a second volume.

Probability distributions are a fundamental topic of Statistics and Data Science that is highly relevant in both theory and practical applications. There are numerous probability distributions that come in many shapes and with different properties. In order to identify an appropriate distribution for modeling the statistical properties of a population of interest, one should consider the shape of the distribution as the crucial factor. In particular, the symmetry or asymmetry of the distribution plays a decisive role.

We welcome submissions related to the latest developments in the area of symmetrical and asymmetrical distributions in Statistics and Data Science. This includes articles that directly or indirectly deal with probability distributions and their symmetry properties. The Special Issue aims to highlight the importance of symmetrical and asymmetrical distributions in its thematic breadth and with applications related.

Welcome to read the publications in "Symmetrical and Asymmetrical Distributions in Statistics and Data Science".

Dr. Arne Johannssen
Dr. Nataliya Chukhrova
Prof. Dr. Quanxin Zhu
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

  • Artificial Intelligence
  • computational statistics
  • data science
  • hypothesis testing
  • machine learning
  • parameter estimation
  • probability distributions
  • skewness
  • statistical data analysis
  • statistical inference

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Related Special Issue

Published Papers (6 papers)

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Research

22 pages, 495 KiB  
Article
Comparing Confidence Intervals for the Mean of Symmetric and Skewed Distributions
by Kristina Veljkovic
Symmetry 2024, 16(11), 1424; https://doi.org/10.3390/sym16111424 - 25 Oct 2024
Viewed by 929
Abstract
In context-aware decision analysis, mean can be an important measure, even when the distribution is skewed. Previous comparative studies showed that it is a real challenge to construct a confidence interval that performs well for highly skewed data. In this study, we propose [...] Read more.
In context-aware decision analysis, mean can be an important measure, even when the distribution is skewed. Previous comparative studies showed that it is a real challenge to construct a confidence interval that performs well for highly skewed data. In this study, we propose new confidence intervals for the population mean based on Edgeworth expansion that include both skewness and kurtosis corrections. We compared existing and newly proposed confidence intervals for a range of samples from symmetric and skewed distributions of varying levels of kurtosis. Using Monte Carlo simulations, we evaluated the performance of these intervals based on the coverage probability, mean length, and standard deviation of the length. The proposed bootstrap Edgeworth-based confidence interval outperformed other confidence intervals in terms of coverage probability for both symmetric and skewed distributions and can be recommended for general use in practice. Full article
(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science II)
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24 pages, 3301 KiB  
Article
Statistical Analysis and Several Estimation Methods of New Alpha Power-Transformed Pareto Model with Applications in Insurance
by Meshayil M. Alsolmi, Fatimah A. Almulhim, Meraou Mohammed Amine, Hassan M. Aljohani, Amani Alrumayh and Fateh Belouadah
Symmetry 2024, 16(10), 1367; https://doi.org/10.3390/sym16101367 - 14 Oct 2024
Viewed by 609
Abstract
This article defines a new distribution using a novel alpha power-transformed method extension. The model obtained has three parameters and is quite effective in modeling skewed, complex, symmetric, and asymmetric datasets. The new approach has one additional parameter for the model. Certain distributional [...] Read more.
This article defines a new distribution using a novel alpha power-transformed method extension. The model obtained has three parameters and is quite effective in modeling skewed, complex, symmetric, and asymmetric datasets. The new approach has one additional parameter for the model. Certain distributional and mathematical properties are investigated, notably reliability, quartile, moments, skewness, kurtosis, and order statistics, and several approaches of estimation, notably the maximum likelihood, least square, weighted least square, maximum product spacing, Cramer-Von Mises, and Anderson Darling estimators of the model parameters were obtained. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed techniques of estimation of the model parameters. The actuarial measures are computed for our recommended model. At the end of the paper, two insurance applications are illustrated to check the potential and utility of the suggested distribution. Evaluation using four selection criteria indicates that our recommended model is the most appropriate probability model for modeling insurance datasets. Full article
(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science II)
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16 pages, 1622 KiB  
Article
Improving the Robustness of the Theil-Sen Estimator Using a Simple Heuristic-Based Modification
by Artur Bal
Symmetry 2024, 16(6), 698; https://doi.org/10.3390/sym16060698 - 5 Jun 2024
Cited by 2 | Viewed by 950
Abstract
One of the most widely used robust regression methods for solving simple linear regression problems is the Theil-Sen (TS) estimator. This estimator has some notable advantages; however, it does not belong to the most robust estimation methods (called high-breakdown estimators) and is prone [...] Read more.
One of the most widely used robust regression methods for solving simple linear regression problems is the Theil-Sen (TS) estimator. This estimator has some notable advantages; however, it does not belong to the most robust estimation methods (called high-breakdown estimators) and is prone to outliers whose distribution is highly asymmetric with respect to the correct data points. This paper presents a modification of the TS estimator, the Robustified Theil-Sen (RTS) estimator. The new method uses a heuristic-based selection procedure to reduce the number of initial estimates of the regression function parameters computed with at least one outlier, thereby improving the regression results. The use of this heuristic procedure only slightly increases the computational time required for using the RTS estimator compared to the TS estimator. Preliminary results of two numerical experiments presented in the paper show that the RTS estimator outperforms other comparable estimators, i.e., the TS estimator and the repeated median estimator, in terms of robustness. The results presented also suggest that the breakpoint value (which is a measure of the robustness of estimators) of the RTS estimator is higher than the breakpoint value of the TS estimator and equal to the breakpoint value of the high-breakpoint estimators. Full article
(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science II)
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22 pages, 4693 KiB  
Article
Bayesian Inference for the Gamma Zero-Truncated Poisson Distribution with an Application to Real Data
by Patchanok Srisuradetchai and Ausaina Niyomdecha
Symmetry 2024, 16(4), 417; https://doi.org/10.3390/sym16040417 - 2 Apr 2024
Cited by 1 | Viewed by 1423
Abstract
This article presents Bayesian estimation methods applied to the gamma zero-truncated Poisson (GZTP) and the complementary gamma zero-truncated Poisson (CGZTP) distributions, encompassing both one-parameter and two-parameter models. These distributions are notably flexible and useful for modeling lifetime data. In the one-parameter model case, [...] Read more.
This article presents Bayesian estimation methods applied to the gamma zero-truncated Poisson (GZTP) and the complementary gamma zero-truncated Poisson (CGZTP) distributions, encompassing both one-parameter and two-parameter models. These distributions are notably flexible and useful for modeling lifetime data. In the one-parameter model case, the Jeffreys prior is mathematically derived. The use of informative and noninformative priors, combined with the random walk Metropolis algorithm within a Bayesian framework, generates samples from the posterior distributions. Bayesian estimators’ effectiveness is examined through extensive simulation studies, in comparison with the maximum likelihood method. Results indicate that Bayesian estimators provide more precise parameter estimates, even with smaller sample sizes. Furthermore, the study and comparison of the coverage probabilities (CPs) and average lengths (ALs) of the credible intervals with those from Wald intervals suggest that Bayesian credible intervals typically yield shorter ALs and higher CPs, thereby demonstrating the effectiveness of Bayesian inference in the context of GZTP and CGZTP distributions. Lastly, Bayesian inference is applied to real data. Full article
(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science II)
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20 pages, 545 KiB  
Article
Statistical Inference and Application of Asymmetrical Generalized Pareto Distribution Based on Peaks-Over-Threshold Model
by Wenru Chen, Xu Zhao, Mi Zhou, Haiqing Chen, Qingqing Ji and Weihu Cheng
Symmetry 2024, 16(3), 365; https://doi.org/10.3390/sym16030365 - 18 Mar 2024
Viewed by 1605
Abstract
Generalized Pareto distribution (GPD), an asymmetrical distribution, primarily models exceedances over a high threshold in many applications. Within the peaks-over-threshold (POT) framework, we consider a new GPD parameter estimation method to estimate a common tail risk measure, the value at risk (VaR). The [...] Read more.
Generalized Pareto distribution (GPD), an asymmetrical distribution, primarily models exceedances over a high threshold in many applications. Within the peaks-over-threshold (POT) framework, we consider a new GPD parameter estimation method to estimate a common tail risk measure, the value at risk (VaR). The proposed method is more suitable for the POT framework and makes full use of data information. Specifically, our estimation method builds upon the generalized probability weighted moments method and integrates it with the nonlinear weighted least squares method. We use exceedances for the GPD, minimizing the sum of squared differences between the sample and population moments of a function of GPD random variables. At the same time, the proposed estimator uses three iterations and assigns weight to further improving the estimated performance. Under Monte Carlo simulations and with a real heavy-tailed dataset, the simulation results show the advantage of the newly proposed estimator, particularly when VaRs are at high confidence levels. In addition, by simulating other heavy-tailed distributions, our method still exhibits good performance in estimating misjudgment distributions. Full article
(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science II)
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14 pages, 2490 KiB  
Article
Applying Generalized Type-II Hybrid Censored Samples on Generalized and q-Generalized Extreme Value Distributions under Linear Normalization
by Rasha Abd El-Wahab Attwa and Taha Radwan
Symmetry 2023, 15(10), 1869; https://doi.org/10.3390/sym15101869 - 5 Oct 2023
Viewed by 1005
Abstract
The generalized extreme value (GEV) distributions have wide applications for describing a variety of random events, such as those that occur during specific survival, financial, or reliability investigations. Also, the q-analogues of GEV distributions, called (q-GEVs), are characterized by their ability to provide [...] Read more.
The generalized extreme value (GEV) distributions have wide applications for describing a variety of random events, such as those that occur during specific survival, financial, or reliability investigations. Also, the q-analogues of GEV distributions, called (q-GEVs), are characterized by their ability to provide more flexibility for modeling, which is due to the influence of the q parameter. In this study, we estimated the parameters of generalized and q-generalized extreme value distributions under linear normalization, called GEVL and q-GEVL, respectively. These parameters were estimated using the maximum likelihood estimator method and are based on the generalized type-II hybrid censored sample (G-Type-II HCS). The confidence intervals for these parameters were evaluated. Also, Shannon entropy was estimated for GEVL and q-GEVL distributions. The accuracy of these parameters and the performance of estimators were demonstrated through a real-life example and a simulation study. Full article
(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science II)
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