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Symmetry
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Symmetry in Statistics and Data Science, Volume 2
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Symmetry in Statistics and Data Science, Volume 2

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 13533

Special Issue Editor

Dr. Christophe Chesneau

E-Mail Website
Guest Editor
Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France
Interests: mathematical statistics; applied statistics; data analysis; probability; applied probability; analytic inequalities
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetry is a central notion in statistics and data science, appearing in various forms in artificial intelligence, data analysis, distribution theory, modeling, networks, nonparametric estimation, parametric estimation, high dimensional data, statistical tests, as well as in many other branches of modern interest. The objective of this Special Issue is to publish highly motivated, original, and innovative research articles that use the notion of symmetry on current topics in statistics and data science.

The scope includes but is not limited to the following topics:

  • Artificial intelligence;
  • Bayes methods;  
  • Data analysis;
  • Dimension reduction and variable selection;
  • Distribution theory;
  • Econometrics;
  • Estimation;
  • Inference with high-dimensional data;
  • Inference of stochastic processes;
  • Machine learning;
  • Modelling;
  • Nonparametric function estimation;
  • Sample surveys;
  • Statistical algorithms;
  • Statistical methods for imaging;
  • Time series analysis.

Dr. Christophe Chesneau
Guest Editor

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.

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

Published Papers (8 papers)

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Research

39 pages, 962 KiB  
Article
A New Tangent-Generated Probabilistic Approach with Symmetrical and Asymmetrical Natures: Monte Carlo Simulation with Reliability Applications
by Huda M. Alshanbari, Hazem Al-Mofleh, Jin-Taek Seong and Saima K. Khosa
Symmetry 2023, 15(11), 2066; https://doi.org/10.3390/sym15112066 - 14 Nov 2023
Cited by 5 | Viewed by 944
Abstract
It is proven evidently that probability distributions have a significant role in data modeling for decision-making. Due to the indispensable role of probability distributions for data modeling in applied fields, a series of probability distributions have been introduced and implemented. However, most newly [...] Read more.
It is proven evidently that probability distributions have a significant role in data modeling for decision-making. Due to the indispensable role of probability distributions for data modeling in applied fields, a series of probability distributions have been introduced and implemented. However, most newly developed probability distributions involve between one and eight additional parameters. Sometimes the additional parameters lead to re-parametrization problems. Therefore, the development of new probability distributions without additional parameters is an interesting research topic. In this paper, we study a new probabilistic method without incorporating any additional parameters. The proposed approach is based on a tangent function and may be called a new tangent-G (NT-G) family of distributions. Certain properties of the NT-G distributions are derived. Based on the NT-G method, a new flexible probability distribution called a new tangent flexible Weibull (NTF-Weibull) distribution is studied. The parameters of the NTF-Weibull distribution are estimated using seven different estimation methods. Based on these eight estimations, a brief simulation of the NTF-Weibull distribution is also provided. Finally, we prove the applicability of the NTF-Weibull distribution by analyzing two waiting-time data sets taken from the reliability sector. We consider three statistical tests with a p-value to evaluate the performance and goodness of fit of the NTF-Weibull distribution. Full article
(This article belongs to the Special Issue Symmetry in Statistics and Data Science, Volume 2)
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16 pages, 345 KiB  
Article
Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine
by Neriman Akdam
Symmetry 2023, 15(9), 1754; https://doi.org/10.3390/sym15091754 - 13 Sep 2023
Cited by 5 | Viewed by 1618
Abstract
The aim of this study is to obtain the Bayes estimators and the maximum likelihood estimators (MLEs) for the unknown parameters of the Rayleigh–Weibull (RW) distribution based on progressive type-II censored samples. The approximate Bayes estimators are calculated using the idea of Lindley, [...] Read more.
The aim of this study is to obtain the Bayes estimators and the maximum likelihood estimators (MLEs) for the unknown parameters of the Rayleigh–Weibull (RW) distribution based on progressive type-II censored samples. The approximate Bayes estimators are calculated using the idea of Lindley, Tierney–Kadane approximations, and also the Markov Chain Monte Carlo (MCMC) method under the squared-error loss function when the Bayes estimators are not handed in explicit forms. In this study, the approximate Bayes estimates are compared with the maximum likelihood estimates in the aspect of the estimated risks (ERs) using Monte Carlo simulation. The asymptotic confidence intervals for the unknown parameters are obtained using the MLEs of parameters. In addition, the coverage probabilities the parametric bootstrap estimates are computed. Real lifetime datasets related to bladder cancer, head and neck cancer, and leukemia are used to illustrate the empirical results belonging to the approximate Bayes estimates, the maximum likelihood estimates, and the parametric bootstrap intervals. Full article
(This article belongs to the Special Issue Symmetry in Statistics and Data Science, Volume 2)
23 pages, 1186 KiB  
Article
A New Statistical Technique to Enhance MCGINAR(1) Process Estimates under Symmetric and Asymmetric Data: Fuzzy Time Series Markov Chain and Its Characteristics
by Mohammed H. El-Menshawy, Abd El-Moneim A. M. Teamah, Mohamed S. Eliwa, Laila A. Al-Essa, Mahmoud El-Morshedy and Rashad M. EL-Sagheer
Symmetry 2023, 15(8), 1577; https://doi.org/10.3390/sym15081577 - 13 Aug 2023
Cited by 1 | Viewed by 1268
Abstract
Several models for time series with integer values have been published as a result of the substantial demand for the description of process stability having discrete marginal distributions. One of these models is the mixed count geometric integer autoregressive of order one (MCGINAR(1)), [...] Read more.
Several models for time series with integer values have been published as a result of the substantial demand for the description of process stability having discrete marginal distributions. One of these models is the mixed count geometric integer autoregressive of order one (MCGINAR(1)), which is based on two thinning operators. This study examines how the estimates of the spectral density functions of the MCGINAR(1) model are affected by fuzzy time series Markov chain (FTSMC). Regarding this study’s context, the higher-order moments, central moments and spectral density functions of MCGINAR(1) are computed. The anticipated realizations of the generated realizations for this model are obtained based on FTSMC. In the case of generated and anticipated realizations, several lag windows are used to smooth the spectral density estimators. The generated realization estimates are compared with the anticipated realization estimates using the MSE to ascertain the FTSMC’s role in improving the estimation process. Full article
(This article belongs to the Special Issue Symmetry in Statistics and Data Science, Volume 2)
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23 pages, 2063 KiB  
Article
Bayesian Estimation for the Difference between Coefficients of Quartile Variation of Delta-Lognormal Distributions: An Application to Rainfall in Thailand
by Noppadon Yosboonruang and Sa-Aat Niwitpong
Symmetry 2023, 15(7), 1383; https://doi.org/10.3390/sym15071383 - 7 Jul 2023
Viewed by 1454
Abstract
The coefficient of quartile variation is a valuable measure used to assess data dispersion when it deviates from a normal distribution or displays skewness. In this study, we focus specifically on the delta-lognormal distribution. The lognormal distribution is characterized by its asymmetrical nature [...] Read more.
The coefficient of quartile variation is a valuable measure used to assess data dispersion when it deviates from a normal distribution or displays skewness. In this study, we focus specifically on the delta-lognormal distribution. The lognormal distribution is characterized by its asymmetrical nature and comprises exclusively positive values. However, when these values undergo a logarithmic transformation, they conform to a symmetrical (or normal) distribution. Consequently, this research aims to establish confidence intervals for the difference between coefficients of quartile variation within lognormal distributions incorporating zero values. We employ the Bayesian, generalized confidence interval, and fiducial generalized confidence interval methods to construct these intervals, involving data simulation using RStudio software. We evaluate the performance of these methods based on coverage probabilities and average lengths. Our findings indicate that the Bayesian method, employing Jeffreys’ prior, performs well in low variability, while the generalized confidence interval method is more suitable for higher variability. Therefore, we recommend using both approaches to construct confidence intervals for the difference between the coefficients of the quartile variation in lognormal distributions that include zero values. Furthermore, we apply these methods to rainfall data in Thailand to illustrate their alignment with actual and simulated data. Full article
(This article belongs to the Special Issue Symmetry in Statistics and Data Science, Volume 2)
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21 pages, 403 KiB  
Article
The Modified-Lomax Distribution: Properties, Estimation Methods, and Application
by Badr Alnssyan
Symmetry 2023, 15(7), 1367; https://doi.org/10.3390/sym15071367 - 5 Jul 2023
Cited by 2 | Viewed by 3035
Abstract
This paper introduces a flexible three-parameter extension of the Lomax model called the odd Lomax–Lomax (OLxLx) distribution. The OLxLx distribution can provide left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, constant, unimodal, and decreasing hazard rate shapes. Some mathematical properties of the [...] Read more.
This paper introduces a flexible three-parameter extension of the Lomax model called the odd Lomax–Lomax (OLxLx) distribution. The OLxLx distribution can provide left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, constant, unimodal, and decreasing hazard rate shapes. Some mathematical properties of the introduced model are derived. The OLxLx density can be expressed as mixture of Lomax densities. The OLxLx parameters are estimated by using eight estimation methods and their performance is explored by using detailed simulation studies. The partial and overall ranks of the mean relative errors, absolute biases, and mean square errors of different estimators are presented to choose the best estimation method. The flexibility and applicability of the OLxLx distribution is shown using real-life medicine data, illustrating the superior fit of the OLxLx distribution over other competing Lomax distributions. The OLxLX distribution outperforms some rival Lomax distributions including the Kumaraswamy–Lomax, McDonald–Lomax, Weibull–Lomax, transmuted Weibull–Lomax, exponentiated-Lomax, Lomax–Weibull, modified Kies–Lomax, Burr X Lomax, beta exponentiated-Lomax, odd exponentiated half-logistic Lomax, and transmuted-Lomax distributions, among others. Full article
(This article belongs to the Special Issue Symmetry in Statistics and Data Science, Volume 2)
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24 pages, 1879 KiB  
Article
A New Lomax Extension: Properties, Risk Analysis, Censored and Complete Goodness-of-Fit Validation Testing under Left-Skewed Insurance, Reliability and Medical Data
by Moustafa Salem, Walid Emam, Yusra Tashkandy, Mohamed Ibrahim, M. Masoom Ali, Hafida Goual and Haitham M. Yousof
Symmetry 2023, 15(7), 1356; https://doi.org/10.3390/sym15071356 - 3 Jul 2023
Cited by 11 | Viewed by 1397
Abstract
The idea of symmetry, which is used to describe the shape of a probability distribution, is a key concept in the theory of probability. The use of symmetric and asymmetric distributions is common in statistical inference, decision-making, and probability calculations. This article introduces [...] Read more.
The idea of symmetry, which is used to describe the shape of a probability distribution, is a key concept in the theory of probability. The use of symmetric and asymmetric distributions is common in statistical inference, decision-making, and probability calculations. This article introduces a novel asymmetric model for assessing risks under a skewed claims dataset. The new distribution is also employed for both censored and uncensored validation testing. Four estimation methods, maximum likelihood, ordinary least squares, L-Moment, and Anderson Darling, were used for the risk assessment and analysis. To explain the exposure to risk within actuarial claims data, we introduced five crucial indicators, namely value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and mean excess losses. A numerical and graphical analysis is presented to assess the actuarial risk. Furthermore, the article discusses a newly developed Rao Robson Nikulin statistic for censored and uncensored validation testing. The validation testing also involved the insurance claims dataset. Full article
(This article belongs to the Special Issue Symmetry in Statistics and Data Science, Volume 2)
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25 pages, 1895 KiB  
Article
A New Right-Skewed One-Parameter Distribution with Mathematical Characterizations, Distributional Validation, and Actuarial Risk Analysis, with Applications
by G. G. Hamedani, Hafida Goual, Walid Emam, Yusra Tashkandy, Fiaz Ahmad Bhatti, Mohamed Ibrahim and Haitham M. Yousof
Symmetry 2023, 15(7), 1297; https://doi.org/10.3390/sym15071297 - 21 Jun 2023
Cited by 7 | Viewed by 1410
Abstract
Skewed probability distributions are important when modeling skewed data sets because they provide a way to describe the shape of the distribution and estimate the likelihood of extreme events. Asymmetric probability distributions have the potential to handle and assess problems in actuarial risk [...] Read more.
Skewed probability distributions are important when modeling skewed data sets because they provide a way to describe the shape of the distribution and estimate the likelihood of extreme events. Asymmetric probability distributions have the potential to handle and assess problems in actuarial risk assessment and analysis. To that end, we present a new right-skewed one-parameter distribution. In this work and for this purpose, a right-skewed probability distribution was derived and analyzed. The new distribution outperformed the exponential distribution, the Pareto distribution, the Chen distribution, and others in the field of actuarial risk analysis. Some useful key risk indicators are considered and analyzed to analyze the risks and for comparison with the competitive model. Several actuarial risk functions and indicators are evaluated and analyzed using the U.K. insurance claims data set. The process of risk assessment and analysis was carried out using a comprehensive simulation. For the purposes of distributional validity, a modified chi-squared type test is presented and employed in the testing process. The new, modified chi-squared type test that is used is simply an extension of the Rao–Robson–Nikulin test. In this work, the distributional validity is presented and analyzed under right-skewed censored and uncensored data sets. Full article
(This article belongs to the Special Issue Symmetry in Statistics and Data Science, Volume 2)
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24 pages, 1290 KiB  
Article
An Efficient Stress–Strength Reliability Estimate of the Unit Gompertz Distribution Using Ranked Set Sampling
by Najwan Alsadat, Amal S. Hassan, Mohammed Elgarhy, Christophe Chesneau and Rokaya Elmorsy Mohamed
Symmetry 2023, 15(5), 1121; https://doi.org/10.3390/sym15051121 - 20 May 2023
Cited by 12 | Viewed by 1520
Abstract
In this paper, the estimation of the stress–strength reliability is taken into account when the stress and strength variables have unit Gompertz distributions with a similar scale parameter. The consideration of the unit Gompertz distribution in this context is because of its intriguing [...] Read more.
In this paper, the estimation of the stress–strength reliability is taken into account when the stress and strength variables have unit Gompertz distributions with a similar scale parameter. The consideration of the unit Gompertz distribution in this context is because of its intriguing symmetric and asymmetric properties that can accommodate various histogram proportional-type data shapes. As the main contribution, the reliability estimate is determined via seven frequentist techniques using the ranked set sampling (RSS) and simple random sampling (SRS). The proposed methods are the maximum likelihood, least squares, weighted least squares, maximum product spacing, Cramér–von Mises, Anderson–Darling, and right tail Anderson–Darling methods. We perform a simulation work to evaluate the effectiveness of the recommended RSS-based estimates by using accuracy metrics. We draw the conclusion that the reliability estimates in the maximum product spacing approach have the lowest value compared to other approaches. In addition, we note that the RSS-based estimates are superior to those obtained by a comparable SRS approach. Additional results are obtained using two genuine data sets that reflect the survival periods of head and neck cancer patients. Full article
(This article belongs to the Special Issue Symmetry in Statistics and Data Science, Volume 2)
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