Recent Applications of Statistical and Mathematical Models

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

Deadline for manuscript submissions: 30 November 2026 | Viewed by 827

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Guest Editor
Department of Mathematics, North Carolina A&T State University, Greensboro, NC 27411, USA
Interests: nonparametric statistics; geostatistics; neural networks and machine learning; data science
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Special Issue Information

Dear Colleagues,

This Special Issue is dedicated to exploring the advanced applications of statistical and mathematical models in addressing the complexities of real-world problems. Our aim is to illuminate the intricate interconnections between modeling and a wide array of disciplines, including economics, biology, engineering, and the social sciences.

We invite contributions that span theoretical, computational, simulation-based, and experimental approaches. Topics of interest include, but are not limited to, the following:

  • Statistical and mathematical modeling;
  • Clustering and classification;
  • Machine learning and data science;
  • Time series analysis;
  • Spatial modeling and geographical analysis;
  • Survival analysis;
  • Survey analysis;
  • Risk assessment and management in finance, healthcare, or environmental contexts.

The primary goal of this Special Issue is to advance our knowledge and means of application of statistical and mathematical modeling. We aim to provide a collaborative platform for researchers to share novel methodologies, case studies, and findings that push the boundaries of current practices.

This Special Issue will serve as a timely contribution to existing scholarship, presenting innovative applications and insights into statistical and mathematical modeling. By showcasing real-world use cases and methodological advancements, it will complement and enrich the current body of literature with fresh perspectives and practical solutions.

Dr. Tamer M Elbayoumi
Guest Editor

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Keywords

  • mathematical modeling
  • statistical modeling
  • clustering
  • classification
  • time series analysis
  • spatial analysis
  • machine learning
  • data science
  • survival analysis
  • survey analysis
  • risk assessment
  • risk management

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Published Papers (1 paper)

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31 pages, 13946 KB  
Article
The XLindley Survival Model Under Generalized Progressively Censored Data: Theory, Inference, and Applications
by Ahmed Elshahhat and Refah Alotaibi
Axioms 2026, 15(1), 56; https://doi.org/10.3390/axioms15010056 - 13 Jan 2026
Viewed by 372
Abstract
This paper introduces a novel extension of the classical Lindley distribution, termed the X-Lindley model, obtained by a specific mixture of exponential and Lindley distributions, thereby substantially enriching the distributional flexibility. To enhance its inferential scope, a comprehensive reliability analysis is developed under [...] Read more.
This paper introduces a novel extension of the classical Lindley distribution, termed the X-Lindley model, obtained by a specific mixture of exponential and Lindley distributions, thereby substantially enriching the distributional flexibility. To enhance its inferential scope, a comprehensive reliability analysis is developed under a generalized progressive hybrid censoring scheme, which unifies and extends several traditional censoring mechanisms and allows practitioners to accommodate stringent experimental and cost constraints commonly encountered in reliability and life-testing studies. Within this unified censoring framework, likelihood-based estimation procedures for the model parameters and key reliability characteristics are derived. Fisher information is obtained, enabling the establishment of asymptotic properties of the frequentist estimators, including consistency and normality. A Bayesian inferential paradigm using Markov chain Monte Carlo techniques is proposed by assigning a conjugate gamma prior to the model parameter under the squared error loss, yielding point estimates, highest posterior density credible intervals, and posterior reliability summaries with enhanced interpretability. Extensive Monte Carlo simulations, conducted under a broad range of censoring configurations and assessed using four precision-based performance criteria, demonstrate the stability and efficiency of the proposed estimators. The results reveal low bias, reduced mean squared error, and shorter interval lengths for the XLindley parameter estimates, while maintaining accurate coverage probabilities. The practical relevance of the proposed methodology is further illustrated through two real-life data applications from engineering and physical sciences, where the XLindley model provides a markedly improved fit and more realistic reliability assessment. By integrating an innovative lifetime model with a highly flexible censoring strategy and a dual frequentist–Bayesian inferential framework, this study offers a substantive contribution to modern survival theory. Full article
(This article belongs to the Special Issue Recent Applications of Statistical and Mathematical Models)
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