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Special Issue "Mathematical and Statistical Analysis Methods with Multidisciplinary Applications"

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

Deadline for manuscript submissions: 30 June 2023 | Viewed by 3245

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Special Issue Editor

Dr. Ehsan Nazemi

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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 1600 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 (5 papers)

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Research

Open AccessArticle

James Stein Estimator for the Beta Regression Model with Application to Heat-Treating Test and Body Fat Datasets

and

Axioms 2023, 12(6), 526; https://doi.org/10.3390/axioms12060526 - 27 May 2023

Viewed by 417

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 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)

Open AccessArticle

A New Reliability Class-Test Statistic for Life Distributions under Convolution, Mixture and Homogeneous Shock Model: Characterizations and Applications in Engineering and Medical Fields

and

Axioms 2023, 12(4), 331; https://doi.org/10.3390/axioms12040331 - 29 Mar 2023

Viewed by 508

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 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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Open AccessArticle

Modeling COVID-19 Real Data Set by a New Extension of Haq Distribution

Mahmoud M. Abd El-Raouf

and

Md Moyazzem Hossain

Axioms 2023, 12(4), 327; https://doi.org/10.3390/axioms12040327 - 28 Mar 2023

Viewed by 632

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. 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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Open AccessArticle

One-Stage Multiple Comparisons of the Mean Lifetimes of k Treatments with the Average for Exponential Distributions under Heteroscedasticity

Shu-Fei Wu

Axioms 2023, 12(3), 312; https://doi.org/10.3390/axioms12030312 - 21 Mar 2023

Viewed by 450

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 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)

Open AccessArticle

Analysis of

ℝ = P [Y < X < Z]

Using Ranked Set Sampling for a Generalized Inverse Exponential Model

and

Axioms 2023, 12(3), 302; https://doi.org/10.3390/axioms12030302 - 15 Mar 2023

Cited by 1 | Viewed by 670

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.

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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Special Issue "Mathematical and Statistical Analysis Methods with Multidisciplinary Applications"

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