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Advances of Applied Probability and Statistics, 2nd Edition
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Advances of Applied Probability and Statistics, 2nd Edition

A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 31 May 2027 | Viewed by 1307

Editors

Dr. Massimiliano Giacalone

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Guest Editor
Department of Economics, University of Campania “Luigi Vanvitelli”, 80143 Capua, Italy
Interests: probability; big data; inference; social science; finance
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Karina Gibert

E-Mail Website
Guest Editor
Research Group on Knowledge Engineering and Machine Learning at Intelligent Data Science and Artificial Intelligence Research Center, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain
Interests: big data; statistics; artificial intelligence; machine learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Following the success and scientific impact of the first edition, this Special Issue aims to continue fostering interdisciplinary research in the broad and rapidly evolving fields of applied probability and statistics. The increasing availability of complex, high-dimensional, heterogeneous and large-scale data across scientific, economic, social, biomedical, industrial and technological domains requires the development of innovative probabilistic and statistical methodologies capable of supporting modern decision-making processes and data-driven systems.

This second edition welcomes original research articles, methodological contributions, computational developments and applied studies addressing recent advances in probability, statistics, machine learning, artificial intelligence, data science, stochastic modeling and statistical inference. Particular attention will be devoted to contributions integrating rigorous theoretical foundations with practical applications in real-world scenarios.

Topics of interest include, but are not limited to, the following: probabilistic modeling; stochastic processes; statistical learning; Bayesian and nonparametric inference; multivariate analysis; permutation and resampling methods; robust statistics; statistical methods for big data; explainable artificial intelligence; predictive analytics; computational statistics; uncertainty quantification; financial and actuarial modeling; environmental and social statistics; statistical methods for health sciences and epidemiology; network analysis; complex systems and interdisciplinary applications involving artificial intelligence and data-driven technologies.

The Special Issue also encourages contributions exploring the interaction between statistical sciences and emerging areas such as smart systems, sustainability, digital transformation, economics, social sciences and biomedical innovation.

Our goal is to provide an international platform for researchers, practitioners and scholars to disseminate high-quality contributions advancing both the theoretical and applied dimensions of probability and statistics in contemporary scientific research.

We look forward to receiving your valuable contributions.

Dr. Massimiliano Giacalone
Prof. Dr. Karina Gibert
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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

  • applied probability
  • applied statistics
  • stochastic processes
  • statistical inference
  • machine learning
  • artificial intelligence
  • big data analytics
  • computational statistics
  • multivariate analysis
  • nonparametric methods
  • permutation tests
  • Bayesian statistics
  • predictive modeling
  • data science
  • uncertainty quantification
  • interdisciplinary applications

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Related Special Issue

Published Papers (3 papers)

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28 pages, 526 KB  
Article
Cumulative Generalized Entropies of Mathai–Haubold Type and Moment Functions of Order Statistics
by Badr S. Alnssyan and Javid Gani Dar
Mathematics 2026, 14(17), 3094; https://doi.org/10.3390/math14173094 - 28 Aug 2026
Viewed by 270
Abstract
The cumulative Mathai–Haubold residual entropy (CMHRE) and cumulative Mathai–Haubold entropy (CMHCE) are introduced as one-parameter extensions of cumulative residual entropy (CRE) and cumulative entropy (CE), respectively. By expanding the integrands using a generalized binomial series and applying moment identities for order statistics, both [...] Read more.
The cumulative Mathai–Haubold residual entropy (CMHRE) and cumulative Mathai–Haubold entropy (CMHCE) are introduced as one-parameter extensions of cumulative residual entropy (CRE) and cumulative entropy (CE), respectively. By expanding the integrands using a generalized binomial series and applying moment identities for order statistics, both measures are represented as absolutely convergent weighted sums involving differences between the expected maxima and minima of independent and identically distributed samples. Generalized weighted versions are also developed using an arbitrary nonnegative weight function, leading to representations in terms of weighted moments of extreme order statistics. Closed-form expressions are obtained for exponential and uniform distributions, while additional examples demonstrate the effects of power and logarithmic weight functions. Three application oriented examples, involving an excess-of-loss insurance layer, a quadratic warranty-cost weight, and a discounted maintenance-cost weight, further illustrate the practical relevance of the proposed measures. A comparison with PDF-based weighted entropies, together with numerical and graphical analyses, is also provided. Full article
(This article belongs to the Special Issue Advances of Applied Probability and Statistics, 2nd Edition)
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33 pages, 1869 KB  
Article
Bayesian Estimation for the Single Coefficient of Variation of Zero-Inflated Two-Parameter Rayleigh Distribution
by Sasipong Kijsason, Sa-Aat Niwitpong and Suparat Niwitpong
Mathematics 2026, 14(17), 3056; https://doi.org/10.3390/math14173056 - 25 Aug 2026
Viewed by 294
Abstract
Real data such as road traffic mortality rates and lifetime observations are often zero-inflated and right-skewed. The zero-inflated two-parameter Rayleigh (ZITR) distribution is employed to model such data in this study. The coefficient of variation (CV) is a statistical measure that is used [...] Read more.
Real data such as road traffic mortality rates and lifetime observations are often zero-inflated and right-skewed. The zero-inflated two-parameter Rayleigh (ZITR) distribution is employed to model such data in this study. The coefficient of variation (CV) is a statistical measure that is used to quantify the relative dispersion of a population, by comparing the standard deviation with the mean. It is widely used to evaluate variability and facilitate comparisons among datasets with different scales or measurement units. This study develops and evaluates seven methods for constructing confidence intervals for the single CV of the ZITR distribution. Three proposed approaches, including Bayesian Markov chain Monte Carlo (MCMC), Bayesian highest posterior density (HPD), and approximate normal (AN) methods, are compared with three existing approaches: generalized confidence interval (GCI), percentile bootstrap (PB), and bootstrap with standard error (BS). Monte Carlo simulations are employed to assess the efficacy of these methods in terms of expected length (EL) and coverage probability (CP). The simulation results show that the HPD method gives acceptable CP with shorter interval lengths than other methods. Moreover, the proposed methods are illustrated with road traffic mortality rates per 100,000 population collected in January 2026 from the Phichit, Suphan Buri, and Prachuap Khiri Khan provinces in Thailand. The results indicate the applicability of the proposed methods for analyzing zero-inflated and right-skewed data in this real-data example. Full article
(This article belongs to the Special Issue Advances of Applied Probability and Statistics, 2nd Edition)
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29 pages, 585 KB  
Article
A Probability Generating Function Based Goodness-of-Fit Test for the Poisson–Three-Parameter Lindley Distribution
by Francisco Novoa-Muñoz
Mathematics 2026, 14(13), 2308; https://doi.org/10.3390/math14132308 - 30 Jun 2026
Viewed by 433
Abstract
The Poisson–Three-Parameter Lindley (PTPL) distribution constitutes a flexible Poisson mixture model for overdispersed count data, encompassing several classical count distributions as special or limiting cases. Despite its growing use in applied contexts, no formal goodness-of-fit test specifically designed for this distribution is currently [...] Read more.
The Poisson–Three-Parameter Lindley (PTPL) distribution constitutes a flexible Poisson mixture model for overdispersed count data, encompassing several classical count distributions as special or limiting cases. Despite its growing use in applied contexts, no formal goodness-of-fit test specifically designed for this distribution is currently available. In this paper, we propose and study a new goodness-of-fit test for the PTPL model based on a Cramér–von Mises type distance between the empirical and theoretical probability generating functions (PGFs). For polynomial weight functions, the test statistic admits an explicit closed-form representation; in practice, it is computed efficiently via numerical quadrature. The null distribution of the statistic is approximated via parametric bootstrap. We establish theoretical properties of the proposed procedure, including consistency against fixed alternatives and the validity of the bootstrap approximation. Monte Carlo simulations with sample sizes n∈{50, 100, 150, 200, 500} for size evaluation and n∈{100, 250, 500} for power comparisons, as well as weight exponents a∈{0, 1, 2}, show that the empirical size is well controlled at both the 5% and 10% nominal levels, and that the test exhibits competitive power against Poisson, Negative Binomial, COM-Poisson, and Zero-Inflated Poisson alternatives. A real data application to five overdispersed count datasets further illustrates the practical utility of the method. The empirical size is further verified across twelve parameter configurations spanning dispersion indices from 1.37 to 59.33, confirming bootstrap validity under strong overdispersion. Full article
(This article belongs to the Special Issue Advances of Applied Probability and Statistics, 2nd Edition)
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