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Axioms
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Mathematical and Statistical Analysis Methods with Multidisciplinary Applications
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Mathematical and Statistical Analysis Methods with Multidisciplinary Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 9976

Special Issue Editor

Dr. Ehsan Nazemi

E-Mail Website
Guest Editor
1. Department of Mechanical Engineering, Faculty of Engineering and Physical Sciences, Southampton University, Southampton, UK
2. Imec-Vision Lab, Department of Physics, University of Antwerp, B-2610 Antwerp, Belgium
Interests: X-ray and neutron imaging; non-destructive testing; ionizing-radiation-based measuring instruments; electrical-capacitance-based multiphase flow meter; artificial neural network; computational techniques
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

In recent years, it has been proved that mathematics and statistical analysis methods are of high importance in various scientific fields such as engineering, economy, healthcare, and clinical medicine. The scope of this theme issue is to give a general view of the current research in the application of mathematical and statistical analysis methods to engineering, economy, healthcare, and clinical medicine as well as to show how these techniques can help in such important aspects as understanding, prediction, correlation, diagnosing, treatment and data processing. This Special Issue will provide a forum for discussing exciting research on applying various kinds of mathematical and statistical analysis techniques such as neural networks, data mining, feature selection, imaging data processing, correlation analysis, etc. in engineering, economy, healthcare, and medicine fields in a broad sense. 

Dr. Ehsan Nazemi
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. Axioms 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

  • neural networks
  • statistical analysis
  • computational intelligence
  • data mining
  • correlation
  • diagnosis
  • biomarker
  • feature selection
  • diagnosing
  • treatment
  • imaging data processing
  • mental health
  • physical healthcare
  • medicine
  • prediction
  • recognition
  • imaging systems
  • numerical methods

Published Papers (9 papers)

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Research

17 pages, 338 KiB  
Article
Derivative Formulas and Gradient of Functions with Non-Independent Variables
by Matieyendou Lamboni
Axioms 2023, 12(9), 845; https://doi.org/10.3390/axioms12090845 - 30 Aug 2023
Viewed by 507
Abstract
Stochastic characterizations of functions subject to constraints result in treating them as functions with non-independent variables. By using the distribution function or copula of the input variables that comply with such constraints, we derive two types of partial derivatives of functions with non-independent [...] Read more.
Stochastic characterizations of functions subject to constraints result in treating them as functions with non-independent variables. By using the distribution function or copula of the input variables that comply with such constraints, we derive two types of partial derivatives of functions with non-independent variables (i.e., actual and dependent derivatives) and argue in favor of the latter. Dependent partial derivatives of functions with non-independent variables rely on the dependent Jacobian matrix of non-independent variables, which is also used to define a tensor metric. The differential geometric framework allows us to derive the gradient, Hessian, and Taylor-type expansions of functions with non-independent variables. Full article
(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)
24 pages, 912 KiB  
Article
On Entropy Estimation of Inverse Weibull Distribution under Improved Adaptive Progressively Type-II Censoring with Applications
by Farouq Mohammad A. Alam and Mazen Nassar
Axioms 2023, 12(8), 751; https://doi.org/10.3390/axioms12080751 - 30 Jul 2023
Cited by 2 | Viewed by 722
Abstract
This article utilizes improved adaptive progressively Type-II censored data to estimate the entropy of the inverse Weibull distribution. Rényi, q, and Shannon entropy measurements are used to define entropy to achieve this objective. Both point and interval estimations of the entropy quantities [...] Read more.
This article utilizes improved adaptive progressively Type-II censored data to estimate the entropy of the inverse Weibull distribution. Rényi, q, and Shannon entropy measurements are used to define entropy to achieve this objective. Both point and interval estimations of the entropy quantities are investigated through the maximum likelihood and maximum product of spacing methods. Two parametric bootstrap confidence intervals based on the two estimation techniques are also considered for the various entropy measures. A Monte Carlo simulation study is conducted to investigate how estimates behave at various sample sizes and different censoring schemes based on some statistical measurements. The simulations demonstrate that, as anticipated, when the sample size grows, the estimation accuracy also grows. Furthermore, they show that the estimated entropy measures get closer to the actual entropy values when the censoring level decreases. For purposes of explanation, two applications to actual datasets are taken into consideration. The results verified that the adaptive or improved adaptive progressive censoring schemes give more information about data than the conventional progressive censoring scheme in terms of minimum entropy measures. Full article
(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)
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21 pages, 481 KiB  
Article
Constant-Stress Modeling of Log-Normal Data under Progressive Type-I Interval Censoring: Maximum Likelihood and Bayesian Estimation Approaches
by Mohamed Sief, Xinsheng Liu, Mona Hosny and Abd El-Raheem M. Abd El-Raheem
Axioms 2023, 12(7), 710; https://doi.org/10.3390/axioms12070710 - 21 Jul 2023
Viewed by 897
Abstract
This paper discusses inferential approaches for the problem of constant-stress accelerated life testing when the failure data are progressive type-I interval censored. Both frequentist and Bayesian estimations are carried out under the assumption that the log-normal location parameter is nonconstant and follows a [...] Read more.
This paper discusses inferential approaches for the problem of constant-stress accelerated life testing when the failure data are progressive type-I interval censored. Both frequentist and Bayesian estimations are carried out under the assumption that the log-normal location parameter is nonconstant and follows a log-linear life-stress model. The confidence intervals of unknown parameters are also constructed based on asymptotic theory and Bayesian techniques. An analysis of a real data set is combined with a Monte Carlo simulation to provide a thorough assessment of the proposed methods. Full article
(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)
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15 pages, 311 KiB  
Article
Neutrosophic Mean Estimation of Sensitive and Non-Sensitive Variables with Robust Hartley–Ross-Type Estimators
by Abdullah Mohammed Alomair and Usman Shahzad
Axioms 2023, 12(6), 578; https://doi.org/10.3390/axioms12060578 - 11 Jun 2023
Cited by 6 | Viewed by 883
Abstract
Under classical statistics, research typically relies on precise data to estimate the population mean when auxiliary information is available. Outliers can pose a significant challenge in this process. The ultimate goal is to determine the most accurate estimates of the population mean while [...] Read more.
Under classical statistics, research typically relies on precise data to estimate the population mean when auxiliary information is available. Outliers can pose a significant challenge in this process. The ultimate goal is to determine the most accurate estimates of the population mean while minimizing variance. Neutrosophic statistics is a generalization of classical statistics that deals with imprecise, uncertain data. Our research introduces the neutrosophic Hartley–Ross-type ratio estimators for estimating the population mean of neutrosophic data, even in the presence of outliers. We also incorporate neutrosophic versions of several robust regression methods, including LAD, Huber-M, Hampel-M, and Tukey-M. Our approach assumes that the study variable is both non-sensitive and sensitive, meaning that it can cause discomfort to participants during personal interviews, and measurement errors can occur due to dishonest responses. To address potential measurement errors, we propose the use of neutrosophic scrambling response models. Our proposed neutrosophic robust estimators are more effective than existing classical estimators, as confirmed by a computer-based numerical study using real data and simulation. Full article
(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)
15 pages, 316 KiB  
Article
James Stein Estimator for the Beta Regression Model with Application to Heat-Treating Test and Body Fat Datasets
by Muhammad Amin, Hajra Ashraf, Hassan S. Bakouch and Najla Qarmalah
Axioms 2023, 12(6), 526; https://doi.org/10.3390/axioms12060526 - 27 May 2023
Viewed by 1351
Abstract
The beta regression model (BRM) is used when the dependent variable may take continuous values and be bounded in the interval (0, 1), such as rates, proportions, percentages and fractions. Generally, the parameters of the BRM are estimated by the method of maximum [...] Read more.
The beta regression model (BRM) is used when the dependent variable may take continuous values and be bounded in the interval (0, 1), such as rates, proportions, percentages and fractions. Generally, the parameters of the BRM are estimated by the method of maximum likelihood estimation (MLE). However, the MLE does not offer accurate and reliable estimates when the explanatory variables in the BRM are correlated. To solve this problem, the ridge and Liu estimators for the BRM were proposed by different authors. In the current study, the James Stein Estimator (JSE) for the BRM is proposed. The matrix mean squared error (MSE) and the scalar MSE properties are derived and then compared to the available ridge estimator, Liu estimator and MLE. The performance of the proposed estimator is evaluated by conducting a simulation experiment and analyzing two real-life applications. The MSE of the estimators is considered as a performance evaluation criterion. The findings of the simulation experiment and applications indicate the superiority of the suggested estimator over the competitive estimators for estimating the parameters of the BRM. Full article
(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)
16 pages, 381 KiB  
Article
A New Reliability Class-Test Statistic for Life Distributions under Convolution, Mixture and Homogeneous Shock Model: Characterizations and Applications in Engineering and Medical Fields
by Walid B. Etman, Mahmoud El-Morshedy, Mohamed S. Eliwa, Amani Almohaimeed and Rashad M. EL-Sagheer
Axioms 2023, 12(4), 331; https://doi.org/10.3390/axioms12040331 - 29 Mar 2023
Cited by 1 | Viewed by 1168
Abstract
Over the past few decades, a new area of reliability known as classes of life distributions has developed as a result of the creation of metrics for evaluating the success or failure of reliability. This paper proposes a new reliability class-test statistic for [...] Read more.
Over the past few decades, a new area of reliability known as classes of life distributions has developed as a result of the creation of metrics for evaluating the success or failure of reliability. This paper proposes a new reliability class-test statistic for life distributions. In some reliability processes, such as convolution, mixture, and homogeneous shock models, the closure characteristics of the proposed class-test statistic are investigated. To compare the proposed class-test against some competitive tests, the Weibull, linear failure rate (LFR), and Makeham distributions are evaluated. In addition, the relationship between sample size, level of confidence, and critical values is considered to assess the efficacy of the proposed class-test. Furthermore, a Monte Carlo null distribution critical points simulation and some applications of the censored and uncensored data are performed to demonstrate the validity of the proposed class-test in reliability analysis. Full article
(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)
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15 pages, 607 KiB  
Article
Modeling COVID-19 Real Data Set by a New Extension of Haq Distribution
by Yusra Tashkandy, Mahmoud E. Bakr, Ahmed M. Gemeay, Eslam Hussam, Mahmoud M. Abd El-Raouf and Md Moyazzem Hossain
Axioms 2023, 12(4), 327; https://doi.org/10.3390/axioms12040327 - 28 Mar 2023
Cited by 1 | Viewed by 1053
Abstract
Modeling real-life pandemics is very important; this study focuses on introducing a new superior flexible extension of the asymmetric Haq distribution known as the power Haq distribution (PHD). The most fundamental mathematical properties are derived. We determine its parameters using ten estimation methods. [...] Read more.
Modeling real-life pandemics is very important; this study focuses on introducing a new superior flexible extension of the asymmetric Haq distribution known as the power Haq distribution (PHD). The most fundamental mathematical properties are derived. We determine its parameters using ten estimation methods. The asymptotic behavior of its estimators is investigated through simulation, and a comparison is done to find out the most efficient method for estimating the parameters of the distribution under consideration. We use a sample for the COVID-19 data set to evaluate the proposed model’s performance and usefulness in fitting the data set in comparison to other well-known models. Full article
(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)
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11 pages, 284 KiB  
Article
One-Stage Multiple Comparisons of the Mean Lifetimes of k Treatments with the Average for Exponential Distributions under Heteroscedasticity
by Shu-Fei Wu
Axioms 2023, 12(3), 312; https://doi.org/10.3390/axioms12030312 - 21 Mar 2023
Viewed by 823
Abstract
Making use of uniformly minimum-variance unbiased estimators for the parameters of two-parameter exponential distributions and the distribution of pivotal quantities, we propose one-stage multiple comparison procedures for k mean lifetimes with the average under heteroscedasticity. The multiple comparison procedures include one-sided and two-sided [...] Read more.
Making use of uniformly minimum-variance unbiased estimators for the parameters of two-parameter exponential distributions and the distribution of pivotal quantities, we propose one-stage multiple comparison procedures for k mean lifetimes with the average under heteroscedasticity. The multiple comparison procedures include one-sided and two-sided confidence intervals. These intervals can be applied to identify which treatment’s mean lifetime is better than the average or worse than the average in terms of the mean lifetimes of all treatments. Critical values are obtained in order to assure users that the given confidence coefficient has been reached; they are organized in table format for practical and convenient use. An example is provided to demonstrate the proposed techniques, wherein the mean survival times of four different lung cancer categories are compared with the average. Full article
(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)
20 pages, 4619 KiB  
Article
Analysis of ℝ=P[Y<X<Z] Using Ranked Set Sampling for a Generalized Inverse Exponential Model
by Amal S. Hassan, Najwan Alsadat, Mohammed Elgarhy, Christophe Chesneau and Heba F. Nagy
Axioms 2023, 12(3), 302; https://doi.org/10.3390/axioms12030302 - 15 Mar 2023
Cited by 5 | Viewed by 1271
Abstract
In many real-world situations, systems frequently fail due to demanding operating conditions. In particular, when systems reach their lowest, highest, or both extremes operating conditions, they usually fail to accomplish their intended functions. This study considers estimating the stress–strength reliability, for a component [...] Read more.
In many real-world situations, systems frequently fail due to demanding operating conditions. In particular, when systems reach their lowest, highest, or both extremes operating conditions, they usually fail to accomplish their intended functions. This study considers estimating the stress–strength reliability, for a component with a strength (X) that is independent of the opposing lower bound stress (Y) and upper bound stress (Z). We assumed that the strength and stress random variables followed a generalized inverse exponential distribution with different shape parameters. Under ranked set sampling (RSS) and simple random sampling (SRS) designs, we obtained four reliability estimators using the maximum likelihood method. The first and second reliability estimators were deduced when the sample data of the strength and stress distributions used the sample design (RSS/SRS). The third reliability estimator was determined when the sample data for Y and Z were received from the RSS and the sample data for X were taken from the SRS. The fourth reliability estimator was derived when the sample data of Y and Z were selected from the SRS, while the sample data of X were taken from the RSS. The accuracy of the suggested estimators was compared using a comprehensive computer simulation. Lastly, three real data sets were used to determine the reliability. Full article
(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)
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