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

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 27352

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Dr. Arne Johannssen

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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
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Dr. Nataliya Chukhrova

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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

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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,

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, but not limited, to Actuarial Sciences, Biology, Business, Economics, Finance, Game Theory, Marketing, Medicine, Meteorology, Philosophy, Politics, Quality Control, Risk Management, and Sports.

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

Symmetrical and Asymmetrical Distributions in Statistics and Data Science II in Symmetry (6 articles)

Published Papers (14 papers)

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Editorial

Jump to: Research

4 pages, 203 KiB

Open AccessEditorial

Symmetrical and Asymmetrical Distributions in Statistics and Data Science

by Arne Johannssen, Nataliya Chukhrova and Quanxin Zhu

Symmetry 2023, 15(12), 2140; https://doi.org/10.3390/sym15122140 - 1 Dec 2023

Viewed by 1492

Abstract

Probability distributions are a fundamental topic of Statistics and Data Science that is highly relevant in both theory and practical applications [...] Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

Research

Jump to: Editorial

19 pages, 3041 KiB

Open AccessArticle

Reliability Analysis of Kavya Manoharan Kumaraswamy Distribution under Generalized Progressive Hybrid Data

by Refah Alotaibi, Ehab M. Almetwally and Hoda Rezk

Symmetry 2023, 15(9), 1671; https://doi.org/10.3390/sym15091671 - 30 Aug 2023

Cited by 2 | Viewed by 1245

Abstract

Generalized progressive hybrid censoring approaches have been developed to reduce test time and cost. This paper investigates the difficulties associated with estimating the unobserved model parameters and the reliability time functions of the Kavya Manoharan Kumaraswamy (KMKu) distribution based on generalized type-II progressive hybrid censoring using classical and Bayesian estimation techniques. The frequentist estimators’ normal approximations are also used to construct the appropriate estimated confidence intervals for the unknown parameter model. Under symmetrical squared error loss, independent gamma conjugate priors are used to produce the Bayesian estimators. The Bayesian estimators and associated highest posterior density intervals cannot be derived analytically since the joint likelihood function is provided in a complicated form. However, they may be evaluated using Monte Carlo Markov chain (MCMC) techniques. Out of all the censoring choices, the best one is selected using four optimality criteria. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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16 pages, 1153 KiB

Open AccessArticle

The Reliability of Stored Water behind Dams Using the Multi-Component Stress-Strength System

by Hanan Haj Ahmad, Dina A. Ramadan, Mahmoud M. M. Mansour and Mohamed S. Aboshady

Symmetry 2023, 15(3), 766; https://doi.org/10.3390/sym15030766 - 21 Mar 2023

Cited by 4 | Viewed by 1573

Abstract

Dams are essential infrastructure for managing water resources and providing entry to clean water for human needs. However, the construction and maintenance of dams require careful consideration of their reliability and safety, specifically in the event of extreme weather conditions such as heavy rainfall or flooding. In this study, the stress-strength model provides a useful framework for evaluating the reliability of dams and their ability to cope with external stresses such as water pressure, earthquake activity, and erosion. The Shasta reservoir in the United States is a prime example of a dam that requires regular assessment of its reliability to guarantee the safety of communities and infrastructure. The Gumbel Type II distribution has been suggested as a suitable model for fitting the collected data on the stress and strength of the reservoir behind the Shasta dam. Both classical and Bayesian approaches have been used to estimate the reliability function under the multi-component stress-strength model, and Monte Carlo simulation has been employed for parameter estimation. In addition, some measures of goodness-of-fit are employed to examine the suitability of the suggested model. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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18 pages, 468 KiB

Open AccessArticle

Estimation of the Modified Weibull Additive Hazards Regression Model under Competing Risks

by Habbiburr Rehman, Navin Chandra, Takeshi Emura and Manju Pandey

Symmetry 2023, 15(2), 485; https://doi.org/10.3390/sym15020485 - 12 Feb 2023

Cited by 3 | Viewed by 1735

Abstract

The additive hazard regression model plays an important role when the excess risk is the quantity of interest compared to the relative risks, where the proportional hazard model is better. This paper discusses parametric regression analysis of survival data using the additive hazards model with competing risks in the presence of independent right censoring. In this paper, the baseline hazard function is parameterized using a modified Weibull distribution as a lifetime model. The model parameters are estimated using maximum likelihood and Bayesian estimation methods. We also derive the asymptotic confidence interval and the Bayes credible interval of the unknown parameters. The finite sample behaviour of the proposed estimators is investigated through a Monte Carlo simulation study. The proposed model is applied to liver transplant data. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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14 pages, 2167 KiB

Open AccessArticle

An Improved Charting Scheme to Monitor the Process Mean Using Two Supplementary Variables

by Muhammad Arslan, Sadia Anwar, Nevine M. Gunaime, Sana Shahab, Showkat Ahmad Lone and Zahid Rasheed

Symmetry 2023, 15(2), 482; https://doi.org/10.3390/sym15020482 - 11 Feb 2023

Cited by 7 | Viewed by 1326

Abstract

A control chart is the most well-known statistical monitoring tecnique to address unfavourable process parameter (s) changes. Quality practitioners always desire a charting device that promptly identifies the undesired changes in the process. This study intends to design a sensitive homogeneously weighted moving average chart using two supplementary variables (hereafter, TAHWMA). The two supplementary variables are correlated with the study variable in the form of a regression estimator, which is an efficient and unbiased estimator for the process mean. The suggested TAHWMA charting structure is checked out and compared in terms of appearance and non-appearance of multicollinearity amidst the two additional variables. Average run length-related measures are taken as performance measures. It is observed that the proposed TAHWMA scheme performs effectively when the two supplementary variables have no collinearity. A comprehensive comparison between the proposed TAHWMA and existing charts is also carried out, showing the proposed’s supremacy over existing counterparts. For execution purposes, two illustrative examples, one belonging to carbon fibre manufacturing-related data and the other using a simulated dataset and where our simulated dataset belongs to symmetrical distribution, are also presented for the application of the recommended TAHWMA chart. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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24 pages, 14007 KiB

Open AccessArticle

Computational Analysis for Fréchet Parameters of Life from Generalized Type-II Progressive Hybrid Censored Data with Applications in Physics and Engineering

by Refah Alotaibi, Hoda Rezk and Ahmed Elshahhat

Symmetry 2023, 15(2), 348; https://doi.org/10.3390/sym15020348 - 27 Jan 2023

Cited by 10 | Viewed by 1422

Abstract

Generalized progressive hybrid censored procedures are created to reduce test time and expenses. This paper investigates the issue of estimating the model parameters, reliability, and hazard rate functions of the Fréchet (Fr) distribution under generalized Type-II progressive hybrid censoring by making use of the Bayesian estimation and maximum likelihood methods. The appropriate estimated confidence intervals of unknown quantities are likewise built using the frequentist estimators’ normal approximations. The Bayesian estimators are created using independent gamma conjugate priors under the symmetrical squared-error loss. The Bayesian estimators and the associated greatest posterior density intervals cannot be computed analytically since the joint likelihood function is obtained in complex form, but they may be assessed using Monte Carlo Markov chain (MCMC) techniques. Via extensive Monte Carlo simulations, the actual behavior of the proposed estimation methodologies is evaluated. Four optimality criteria are used to choose the best censoring scheme out of all the options. To demonstrate how the suggested approaches may be utilized in real scenarios, two real applications reflecting the thirty successive values of precipitation in Minneapolis–Saint Paul for the month of March as well as the number of vehicle fatalities for thirty-nine counties in South Carolina during 2012 are examined. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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29 pages, 961 KiB

Open AccessArticle

Statistical Analysis of Alpha Power Inverse Weibull Distribution under Hybrid Censored Scheme with Applications to Ball Bearings Technology and Biomedical Data

by Hanan Haj Ahmad, Ehab M. Almetwally, Ahmed Rabaiah and Dina A. Ramadan

Symmetry 2023, 15(1), 161; https://doi.org/10.3390/sym15010161 - 5 Jan 2023

Cited by 4 | Viewed by 1200

Abstract

Applications in medical technology have a massive contribution to the treatment of patients. One of the attractive tools is ball bearings. These balls support the load of the application as well as minimize friction between the surfaces. If a heavy load is applied to a ball bearing, there is the risk that the balls may be damaged and cause the bearing to fail earlier. Hence, we aim to study the model of the failure times of ball bearings. A hybrid Type-II censoring scheme is recommended to minimize the experimental time and cost where the components are following alpha power inverse Weibull distribution. A ball bearing is one example; the other is the resistance of guinea pigs exposed to dosages of virulent tubercle bacilli. We use different estimation methods to obtain point and interval estimates of the unknown parameters of the distribution; consequently, estimating statistical functions such as the hazard rate and the survival functions are observed. The maximum likelihood method and the maximum product spacing methods are used, in addition to the Bayesian estimation method, in which symmetric and asymmetric loss functions are utilized. Interval estimators are obtained for the unknown parameters using three different criteria: approximate, credible, and bootstrap confidence intervals. The performance of the parameters’ estimation is accomplished via simulation analysis and numerical methods such as Newton–Raphson and Monte Carlo Markov chains. Finally, results and conclusions support the suitability of alpha power inverse Weibull distribution under a hybrid Type-II censoring scheme for modeling real biomedical data. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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18 pages, 1519 KiB

Open AccessArticle

Reduction in Waiting Time in an M/M/1/N Encouraged Arrival Queue with Feedback, Balking and Maintaining of Reneged Customers

by Ismailkhan Enayathulla Khan and Rajendran Paramasivam

Symmetry 2022, 14(8), 1743; https://doi.org/10.3390/sym14081743 - 22 Aug 2022

Cited by 14 | Viewed by 2334

Abstract

In this research, we look at the work associated with the encouraged arrival line with feedback, balking and maintaining reneged clients. We analyse the quality control policy for the Markovian model using an iterative method to the nth customer in the system. We derive performance measures for the expected number of units in the system, as well as in the queue and the average number of occupied services and the expected waiting time in the system, as well as in the queue. To show the effectiveness, we provide numerical examples for the average default rate and average retention rate. The developed formula also satisfies Little’s formula. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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13 pages, 1291 KiB

Open AccessArticle

Estimation of Asymmetric Spatial Autoregressive Dependence on Irregular Lattices

by Franz H. Harke, Miryam S. Merk and Philipp Otto

Symmetry 2022, 14(7), 1474; https://doi.org/10.3390/sym14071474 - 19 Jul 2022

Cited by 2 | Viewed by 2030

Abstract

In spatial econometrics, we usually assume that the spatial dependence structure is known and that all information about it is contained in a spatial weights matrix

W

. However, in practice, the structure of

W

is unknown a priori and difficult to obtain, [...] Read more.

In spatial econometrics, we usually assume that the spatial dependence structure is known and that all information about it is contained in a spatial weights matrix

W

. However, in practice, the structure of

W

is unknown a priori and difficult to obtain, especially for asymmetric dependence. In this paper, we propose a data-driven method to obtain

W

, whether it is symmetric or asymmetric. This is achieved by calculating the area overlap of the adjacent regions/districts with a given shape (a pizza-like shape, in our case). With

W

determined in this way, we estimate the potentially asymmetric spatial autoregressive dependence on irregular lattices. We verify our method using Monte Carlo simulations for finite samples and compare it with classical approaches such as Queen’s contiguity matrices and inverse-distance weighting matrices. Finally, our method is applied to model the evolution of sales prices for building land in Brandenburg, Germany. We show that the price evolution and its spatial dependence are mainly driven by the orientation towards Berlin. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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18 pages, 2605 KiB

Open AccessArticle

Generating Optimal Discrete Analogue of the Generalized Pareto Distribution under Bayesian Inference with Applications

by Hanan Haj Ahmad and Ehab M. Almetwally

Symmetry 2022, 14(7), 1457; https://doi.org/10.3390/sym14071457 - 16 Jul 2022

Cited by 7 | Viewed by 1813

Abstract

This paper studies three discretization methods to formulate discrete analogues of the well-known continuous generalized Pareto distribution. The generalized Pareto distribution provides a wide variety of probability spaces, which support threshold exceedances, and hence, it is suitable for modeling many failure time issues. Bayesian inference is applied to estimate the discrete models with different symmetric and asymmetric loss functions. The symmetric loss function being used is the squared error loss function, while the two asymmetric loss functions are the linear exponential and general entropy loss functions. A detailed simulation analysis was performed to compare the performance of the Bayesian estimation using the proposed loss functions. In addition, the applicability of the optimal discrete generalized Pareto distribution was compared with other discrete distributions. The comparison was based on different goodness-of-fit criteria. The results of the study reveal that the discretized generalized Pareto distribution is quite an attractive alternative to other discrete competitive distributions. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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22 pages, 7185 KiB

Open AccessArticle

Monitoring the Ratio of Two Normal Variables Based on Triple Exponentially Weighted Moving Average Control Charts with Fixed and Variable Sampling Intervals

by Xuelong Hu, Guan Sun, Fupeng Xie and Anan Tang

Symmetry 2022, 14(6), 1236; https://doi.org/10.3390/sym14061236 - 14 Jun 2022

Cited by 6 | Viewed by 1813

Abstract

In statistical process control (SPC), the ratio of two normal random variables (RZ) is a valuable statistical indicator to be taken as the charting statistic. In this work, we propose a triple exponentially weighted moving average (TEWMA) chart for monitoring the RZ. Additionally, the variable sampling interval (VSI) strategy has been adopted to different control charts by researchers. With the application of this strategy, the VSI-TEWMA-RZ chart is then developed to further improve the performance of the proposed TEWMA-RZ chart. The run length (RL) properties of the proposed TEWMA-RZ and VSI-TEWMA-RZ charts are obtained by the widely used Monte-Carlo (MC) simulations. Through the comparisons with the VSI-EWMA-RZ and the VSI-DEWMA-RZ charts, the VSI-TEWMA-RZ chart is statistically more sensitive than the VSI-EWMA-RZ and the VSI-DEWMA-RZ charts in detecting small and moderate shifts. Moreover, it turned out that the VSI-TEWMA-RZ chart has better performance than the TEWMA-RZ chart on the whole. Furthermore, this paper illustrates the implementation of the proposed charts with an example from the food industry. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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21 pages, 2820 KiB

Open AccessArticle

Type II Half-Logistic Odd Fréchet Class of Distributions: Statistical Theory and Applications

by Salem A. Alyami, Moolath Girish Babu, Ibrahim Elbatal, Naif Alotaibi and Mohammed Elgarhy

Symmetry 2022, 14(6), 1222; https://doi.org/10.3390/sym14061222 - 13 Jun 2022

Cited by 11 | Viewed by 1893

Abstract

A new class of statistical distributions called the Type II half-Logistic odd Fréchet-G class is proposed. The new class is a continuation of the unusual Fréchet class. This class is analytically feasible and could be used to evaluate real-world data effectively. The new suggested class of distributions has many new symmetrical and asymmetrical sub-models. We propose new four sub-models from the new class of distributions which are called Type II half-Logistic odd Fréchet exponential distribution, Type II half-Logistic odd Fréchet Rayleigh distribution, Type II half-Logistic odd Fréchet Weibull distribution, and Type II half-Logistic odd Fréchet Lindley distribution. Some statistical features of Type II half-Logistic odd Fréchet-G class such as ordinary moments (ORMs), incomplete moments (INMs), moment generating function (MGEF), residual life (REL), and reversed residual life (RREL) functions, and Rényi entropy (RéE) are derived. Six methods of estimation such as maximum likelihood, least-square, a maximum product of spacing, weighted least square, Cramér-von Mises, and Anderson–Darling are produced to estimate the parameters. To test the six estimation methods’ performance, a simulation study is conducted. Four real-world data sets are utilized to highlight the importance and applicability of the proposed method. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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27 pages, 3037 KiB

Open AccessArticle

Copula-Based Estimation Methods for a Common Mean Vector for Bivariate Meta-Analyses

by Jia-Han Shih, Yoshihiko Konno, Yuan-Tsung Chang and Takeshi Emura

Symmetry 2022, 14(2), 186; https://doi.org/10.3390/sym14020186 - 18 Jan 2022

Cited by 16 | Viewed by 3005

Abstract

Traditional bivariate meta-analyses adopt the bivariate normal model. As the bivariate normal distribution produces symmetric dependence, it is not flexible enough to describe the true dependence structure of real meta-analyses. As an alternative to the bivariate normal model, recent papers have adopted “copula” models for bivariate meta-analyses. Copulas consist of both symmetric copulas (e.g., the normal copula) and asymmetric copulas (e.g., the Clayton copula). While copula models are promising, there are only a few studies on copula-based bivariate meta-analysis. Therefore, the goal of this article is to fully develop the methodologies and theories of the copula-based bivariate meta-analysis, specifically for estimating the common mean vector. This work is regarded as a generalization of our previous methodological/theoretical studies under the FGM copula to a broad class of copulas. In addition, we develop a new R package, “CommonMean.Copula”, to implement the proposed methods. Simulations are performed to check the proposed methods. Two real dataset are analyzed for illustration, demonstrating the insufficiency of the bivariate normal model. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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15 pages, 432 KiB

Open AccessArticle

Modified One-Sided EWMA Charts without- and with Variable Sampling Intervals for Monitoring a Normal Process

by Xuelong Hu, Suying Zhang, Guan Sun, Jianlan Zhong and Shu Wu

Symmetry 2022, 14(1), 159; https://doi.org/10.3390/sym14010159 - 13 Jan 2022

Cited by 3 | Viewed by 1752

Abstract

Much research has been conducted on two-sided Exponentially Weighted Moving Average (EWMA) control charts, while less work has been devoted to the one-sided EWMA charts. Traditional one-sided EWMA charts involve resetting the EWMA statistic to the target whenever it falls below or above the target, or truncating the observations above or below the target and further applying the EWMA statistic to the truncated samples. In order to further improve the performance of traditional one-sided EWMA mean (

\bar{X}

) charts, this paper studies the performance of the Modified One-sided EWMA (MOEWMA)

\bar{X}

charts to monitor a normally distributed process. The Monte-Carlo simulation method is used to obtain the zero- and steady-state Run Length (

R L

) properties of the proposed control charts. Through extensive simulations and comparisons with other charts, it is shown that the proposed MOEWMA

\bar{X}

charts compare favorably with some existing competing charts. Moreover, by attaching the variable sampling intervals (VSI) feature to the MOEWMA

\bar{X}

charts, it is shown that the VSI MOEWMA charts outperform the corresponding charts without the VSI feature. Finally, a real data example from manufacturing process shows the implementation of the proposed one-sided charts. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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