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Mathematics
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Statistics and Nonlinear Analysis: Simulation and Computation
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Statistics and Nonlinear Analysis: Simulation and Computation

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 4352

Special Issue Editor

Prof. Dr. Vesna Rajić

E-Mail Website
Guest Editor
Faculty of Economics and Business, University of Belgrade, Kamenička 6, Belgrade, Serbia
Interests: probability and statistics; nonlinear analysis; actuarial mathematics

Special Issue Information

Dear Colleagues,

In this Special Issue, we encourage submissions providing new results in the setting of statistics and nonlinear analysis and their applications.

Statistics and probability are important in many fields such as economy, sociology, psychology, forecasting, etc. Probability theory and distributions are used to define mathematical models in many branches of science. It is important to derive properties of distributions, estimate parameters, derive limit cases, or generalize results. Statistical research includes decision theory, estimation, hypothesis testing, large sample theory, asymptotic efficiency of estimators, exponential families, and sequential analysis. Statistical theory are also important in machine learning and big data science.

Nonlinear analysis is devoted to nonlinear problems from different areas. The purpose of this Special Issue is to gather significant contributions that concern fixed point theory and analysis of partial differential equations as well as their applications to nonlinear analysis and optimization. 

Prof. Dr. Vesna Rajić
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • statistical inference
  • probability theory
  • distribution families
  • machine learning
  • statistical modeling
  • nonlinear analysis
  • fixed point theory
  • partial differential equations

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Published Papers (4 papers)

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Research

29 pages, 3104 KiB  
Article
Dynamical Properties of a Stochastic Tumor–Immune System with Impulsive Perturbations and Regime Switching
by Junfeng Zhao, Bingshuo Wang, Wei Li, Dongmei Huang and Vesna Rajic
Mathematics 2025, 13(6), 928; https://doi.org/10.3390/math13060928 - 11 Mar 2025
Viewed by 395
Abstract
Despite numerous clinical attempts to treat tumors, malignant tumors remain a significant threat to human health due to associated side effects. Consequently, researchers are dedicated to studying the dynamical evolution of tumors in order to provide guidance for therapeutic treatment. This paper presents [...] Read more.
Despite numerous clinical attempts to treat tumors, malignant tumors remain a significant threat to human health due to associated side effects. Consequently, researchers are dedicated to studying the dynamical evolution of tumors in order to provide guidance for therapeutic treatment. This paper presents a stochastic tumor–immune model to discover the role of the regime switching in microenvironments and analyze tumor evolution under comprehensive pulse effects. By selecting an appropriate Lyapunov function and applying Itô’s formula, the ergodicity theory of Markov chains, and inequality analysis methods, we undertake a systematic investigation of a tumor’s behavior, focusing on its extinction, its persistence, and the existence of a stationary distribution. Our detailed analysis uncovers a profound impact of environmental regime switching on the dynamics of tumor cells. Specifically, we find that when the system is subjected to a high-intensity white noise environment over an extended duration, the growth of tumor cells is markedly suppressed. This critical finding reveals the indispensable role of white noise intensity and exposure duration in the long-term evolution of tumors. The tumor cells exhibit a transition from persistence to extinction when the environmental regime switches between two states. Furthermore, the growth factor of the tumor has an essential influence on the steady-state distribution of the tumor evolution. The theoretical foundations in this paper can provide some practical insights to develop more effective tumor treatment strategies, ultimately contributing to advancements in cancer research and care. Full article
(This article belongs to the Special Issue Statistics and Nonlinear Analysis: Simulation and Computation)
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28 pages, 2864 KiB  
Article
Discrete Joint Random Variables in Fréchet-Weibull Distribution: A Comprehensive Mathematical Framework with Simulations, Goodness-of-Fit Analysis, and Informed Decision-Making
by Diksha Das, Tariq S. Alshammari, Khudhayr A. Rashedi, Bhanita Das, Partha Jyoti Hazarika and Mohamed S. Eliwa
Mathematics 2024, 12(21), 3401; https://doi.org/10.3390/math12213401 - 30 Oct 2024
Cited by 2 | Viewed by 881
Abstract
This paper introduces a novel four-parameter discrete bivariate distribution, termed the bivariate discretized Fréchet–Weibull distribution (BDFWD), with marginals derived from the discretized Fréchet–Weibull distribution. Several statistical and reliability properties are thoroughly examined, including the joint cumulative distribution function, joint probability mass function, joint [...] Read more.
This paper introduces a novel four-parameter discrete bivariate distribution, termed the bivariate discretized Fréchet–Weibull distribution (BDFWD), with marginals derived from the discretized Fréchet–Weibull distribution. Several statistical and reliability properties are thoroughly examined, including the joint cumulative distribution function, joint probability mass function, joint survival function, bivariate hazard rate function, and bivariate reversed hazard rate function, all presented in straightforward forms. Additionally, properties such as moments and their related concepts, the stress–strength model, total positivity of order 2, positive quadrant dependence, and the median are examined. The BDFWD is capable of modeling asymmetric dispersion data across various forms of hazard rate shapes and kurtosis. Following the introduction of the mathematical and statistical frameworks of the BDFWD, the maximum likelihood estimation approach is employed to estimate the model parameters. A simulation study is also conducted to investigate the behavior of the generated estimators. To demonstrate the capability and flexibility of the BDFWD, three distinct datasets are analyzed from various fields, including football score records, recurrence times to infection for kidney dialysis patients, and student marks from two internal examination statistical papers. The study confirms that the BDFWD outperforms competitive distributions in terms of efficiency across various discrete data applications. Full article
(This article belongs to the Special Issue Statistics and Nonlinear Analysis: Simulation and Computation)
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24 pages, 3484 KiB  
Article
INLA Estimation of Semi-Variable Coefficient Spatial Lag Model—Analysis of PM2.5 Influencing Factors in the Context of Urbanization in China
by Qiong Pang and Xijian Hu
Mathematics 2024, 12(7), 953; https://doi.org/10.3390/math12070953 - 23 Mar 2024
Viewed by 1289
Abstract
The Semi-variable Coefficient Spatial Lag Model (SVC-SLM) not only addresses the “dimension disaster” associated with the Varying Coefficient Spatial Lag Model(VC-SLM), but also overcomes the non-linear problem of the variable coefficient, and fully explores the hidden information of the model. In this paper, [...] Read more.
The Semi-variable Coefficient Spatial Lag Model (SVC-SLM) not only addresses the “dimension disaster” associated with the Varying Coefficient Spatial Lag Model(VC-SLM), but also overcomes the non-linear problem of the variable coefficient, and fully explores the hidden information of the model. In this paper, INLA is firstly used to estimate the parameters of (SVC-SLM) by using B-spline to deal with the non-parametric terms, and the comparative experimental results show that the INLA algorithm is much better than MCMCINLA in terms of both time efficiency and estimation accuracy. For the problem of identifying the constant coefficient terms in the SVC-SLM, the bootstrap test is given based on the residuals. Taking the PM2.5 data of 31 provinces in mainland China from 2015 to 2020 as an empirical example, parametric, non-parametric, and semi-parametric perspectives establish three models of Spatial Lag Model (SLM), VC-SLM, SVC-SLM, which explore the relationship between the covariate factors and the level of urbanization as well as their impacts on the concentration of PM2.5 in the context of increasing urbanization; among the three models, the SVC-SLM has the smallest values of DIC and WAIC, indicating that the SVC-SLM is optimal. Full article
(This article belongs to the Special Issue Statistics and Nonlinear Analysis: Simulation and Computation)
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14 pages, 1471 KiB  
Article
A Group MCP Approach for Structure Identification in Non-Parametric Accelerated Failure Time Additive Regression Model
by Sumin Hou and Hao Lv
Mathematics 2023, 11(22), 4628; https://doi.org/10.3390/math11224628 - 13 Nov 2023
Cited by 1 | Viewed by 1105
Abstract
In biomedical research, identifying genes associated with diseases is of paramount importance. However, only a small fraction of genes are related to specific diseases among the multitude of genes. Therefore, gene selection and estimation are necessary, and the accelerated failure time model is [...] Read more.
In biomedical research, identifying genes associated with diseases is of paramount importance. However, only a small fraction of genes are related to specific diseases among the multitude of genes. Therefore, gene selection and estimation are necessary, and the accelerated failure time model is often used to address such issues. Hence, this article presents a method for structural identification and parameter estimation based on a non-parametric additive accelerated failure time model for censored data. Regularized estimation and variable selection are achieved using the Group MCP penalty method. The non-parametric component of the model is approximated using B-spline basis functions, and a group coordinate descent algorithm is employed for model solving. This approach effectively identifies both linear and nonlinear factors in the model. The Group MCP penalty estimation exhibits consistency and oracle properties under regularization conditions, meaning that the selected variable set tends to have a probability of approaching 1 and asymptotically includes the actual predictive factors. Numerical simulations and a lung cancer data analysis demonstrate that the Group MCP method outperforms the Group Lasso method in terms of predictive performance, with the proposed algorithm showing faster convergence rates. Full article
(This article belongs to the Special Issue Statistics and Nonlinear Analysis: Simulation and Computation)
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