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Axioms
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Methods and Applications of Advanced Statistical Analysis, 2nd Edition
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Methods and Applications of Advanced Statistical Analysis, 2nd Edition

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

Deadline for manuscript submissions: 26 June 2025 | Viewed by 4471

Special Issue Editor

Dr. Tomas Ruzgas

E-Mail Website
Guest Editor
Department of Applied Mathematics, Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania
Interests: nonparametric statistics; application of functional analysis in statistics; hypothesis testing; multivariate analysis in social, environmental, medical sciences, etc.
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is dedicated to exploring the latest advances in statistical analysis that are innovative in their theoretical, methodological, or applicability approach. Potential topics of interest for this Special Issue include, but are not limited to, survey sampling, nonparametric statistics, functional data analysis, Bayesian analysis, robust statistics, hypothesis testing, univariate and multivariate statistics, regression and analysis of variance, categorical data analysis, classification and clustering, mixed modelling, survival analysis, time series analysis, and their applications.

Dr. Tomas Ruzgas
Guest Editor

Manuscript Submission Information

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Keywords

  • application of statistics
  • causal analysis
  • classification and clustering
  • data analysis
  • linear and nonlinear models
  • mixed modeling
  • nonparametric statistics
  • regression and analysis of variance
  • robust statistics
  • time series

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Related Special Issue

Published Papers (6 papers)

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Research

28 pages, 13036 KiB  
Article
Statistical Analysis of a Generalized Variant of the Weibull Model Under Unified Hybrid Censoring with Applications to Cancer Data
by Mazen Nassar, Refah Alotaibi and Ahmed Elshahhat
Axioms 2025, 14(6), 442; https://doi.org/10.3390/axioms14060442 - 5 Jun 2025
Viewed by 190
Abstract
This paper investigates an understudied generalization of the classical exponential, Rayleigh, and Weibull distributions, known as the power generalized Weibull distribution, particularly in the context of censored data. Characterized by one scale parameter and two shape parameters, the proposed model offers enhanced flexibility [...] Read more.
This paper investigates an understudied generalization of the classical exponential, Rayleigh, and Weibull distributions, known as the power generalized Weibull distribution, particularly in the context of censored data. Characterized by one scale parameter and two shape parameters, the proposed model offers enhanced flexibility for modeling diverse lifetime data patterns and hazard rate behaviors. Notably, its hazard rate function can exhibit five distinct shapes, including upside-down bathtub and bathtub shapes. The study focuses on classical and Bayesian estimation frameworks for the model parameters and associated reliability metrics under a unified hybrid censoring scheme. Methodologies include both point estimation (maximum likelihood and posterior mean estimators) and interval estimation (approximate confidence intervals and Bayesian credible intervals). To evaluate the performance of these estimators, a comprehensive simulation study is conducted under varied experimental conditions. Furthermore, two empirical applications on real-world cancer datasets underscore the efficacy of the proposed estimation methods and the practical viability and flexibility of the explored model compared to eleven other existing lifespan models. Full article
(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 2nd Edition)
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24 pages, 6958 KiB  
Article
Copula-Based Bivariate Modified Fréchet–Exponential Distributions: Construction, Properties, and Applications
by Hanan Haj Ahmad and Dina A. Ramadan
Axioms 2025, 14(6), 431; https://doi.org/10.3390/axioms14060431 - 1 Jun 2025
Viewed by 264
Abstract
The classical exponential model, despite its flexibility, fails to describe data with non-constant failure or between-event dependency. To overcome this limitation, two new bivariate lifetime distributions are introduced in this paper. The Farlie–Gumbel–Morgenstern (FGM)-based and Ali–Mikhail–Haq (AMH)-based modified Fréchet–exponential (MFE) models, by embedding [...] Read more.
The classical exponential model, despite its flexibility, fails to describe data with non-constant failure or between-event dependency. To overcome this limitation, two new bivariate lifetime distributions are introduced in this paper. The Farlie–Gumbel–Morgenstern (FGM)-based and Ali–Mikhail–Haq (AMH)-based modified Fréchet–exponential (MFE) models, by embedding the flexible MEF margin in the FGM and AMH copulas. The resulting distributions accommodate a wide range of positive or negative dependence while retaining analytical traceability. Closed-form expressions for the joint and marginal density, survival, hazard, and reliability functions are derived, together with product moments and moment-generating functions. Unknown parameters are estimated through the maximum likelihood estimation (MLE) and inference functions for margins (IFM) methods, with asymptotic confidence intervals provided for these parameters. An extensive Monte Carlo simulation quantifies the bias, mean squared error, and interval coverage, indicating that IFM retains efficiency while reducing computational complexity for moderate sample sizes. The models are validated using two real datasets, from the medical sector regarding the infection recurrence times of 30 kidney patients undergoing peritoneal dialysis, and from the economic sector regarding the growth of the gross domestic product (GDP). Overall, the proposed copula-linked MFE distributions provide a powerful and economical framework for survival analysis, reliability, and economic studies. Full article
(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 2nd Edition)
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23 pages, 1299 KiB  
Article
Competing Risks in Accelerated Life Testing: A Study on Step-Stress Models with Tampered Random Variables
by Hanan Haj Ahmad, Ehab M. Almetwally and Dina A. Ramadan
Axioms 2025, 14(1), 32; https://doi.org/10.3390/axioms14010032 - 2 Jan 2025
Cited by 1 | Viewed by 826
Abstract
This study introduces a novel approach to accelerated life test experiments by examining competing risk factors using the Tampered Random Variable (TRV) model. This approach remains extensively unexplored in current research. The methodology is implemented for a simple step-stress life test (SSLT) model [...] Read more.
This study introduces a novel approach to accelerated life test experiments by examining competing risk factors using the Tampered Random Variable (TRV) model. This approach remains extensively unexplored in current research. The methodology is implemented for a simple step-stress life test (SSLT) model and accounts for various causes of failure. The Power Chris–Jerry (PCJ) distribution is utilized to model the lifetimes of units under different stress levels, incorporating unique shape parameters while maintaining a fixed-scale parameter. This study employs the TRV model to integrate constant tampering coefficients for each failure cause within step-stress data analysis. Maximum-likelihood estimates for model parameters and tampering coefficients are derived from SSLT data, and some confidence intervals are presented based on the Type-II censoring scheme. Furthermore, Bayesian estimation is applied to the parameters, supported by appropriate prior distributions. The robustness of the proposed method is validated through comprehensive simulations and real-world applications in different scientific domains. Full article
(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 2nd Edition)
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20 pages, 3039 KiB  
Article
Bayesian and Non-Bayesian Inference to Bivariate Alpha Power Burr-XII Distribution with Engineering Application
by Dina A. Ramadan, Mustafa M. Hasaballah, Nada K. Abd-Elwaha, Arwa M. Alshangiti, Mahmoud I. Kamel, Oluwafemi Samson Balogun and Mahmoud M. El-Awady
Axioms 2024, 13(11), 796; https://doi.org/10.3390/axioms13110796 - 17 Nov 2024
Cited by 1 | Viewed by 762
Abstract
In this research, we present a new distribution, which is the bivariate alpha power Burr-XII distribution, based on the alpha power Burr-XII distribution. We thoroughly examine the key features of our newly developed bivariate model. We introduce a new class of bivariate models, [...] Read more.
In this research, we present a new distribution, which is the bivariate alpha power Burr-XII distribution, based on the alpha power Burr-XII distribution. We thoroughly examine the key features of our newly developed bivariate model. We introduce a new class of bivariate models, which are built with the copula function. The statistical properties of the proposed distribution, such as conditional distributions, conditional expectations, marginal distributions, moment-generating functions, and product moments were studied. This was accomplished with two datasets of real data that came from two distinct devices. We employed Bayesian, maximum likelihood estimation, and least squares estimation strategies to obtain estimated points and intervals. Additionally, we generated bootstrap confidence intervals and conducted numerical analyses using the Markov chain Monte Carlo method. Lastly, we compared this novel bivariate distribution’s performance to earlier bivariate models, to determine how well it fit the real data. Full article
(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 2nd Edition)
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14 pages, 455 KiB  
Article
Skew-Symmetric Generalized Normal and Generalized t Distributions
by Najmeh Nakhaei Rad, Mahdi Salehi, Yaser Mehrali and Ding-Geng Chen
Axioms 2024, 13(11), 782; https://doi.org/10.3390/axioms13110782 - 13 Nov 2024
Viewed by 815
Abstract
In this paper, we introduce the skew-symmetric generalized normal and the skew-symmetric generalized t distributions, which are skewed extensions of symmetric special cases of generalized skew-normal and generalized skew-t distributions, respectively. We derive key distributional properties for these new distributions, including a [...] Read more.
In this paper, we introduce the skew-symmetric generalized normal and the skew-symmetric generalized t distributions, which are skewed extensions of symmetric special cases of generalized skew-normal and generalized skew-t distributions, respectively. We derive key distributional properties for these new distributions, including a recurrence relation and an explicit form for the cumulative distribution function (cdf) of the skew-symmetric generalized t distribution. Numerical examples including a simulation study and a real data analysis are presented to illustrate the practical applicability of these distributions. Full article
(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 2nd Edition)
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11 pages, 275 KiB  
Article
Calibration Estimators with Different Types of Distance Measures Under Stratified Sampling in the Presence of Measurement Error
by Sat Gupta and Pidugu Trisandhya
Axioms 2024, 13(11), 737; https://doi.org/10.3390/axioms13110737 - 27 Oct 2024
Viewed by 944
Abstract
The calibration method is used in stratified random sampling in the presence of measurement error to achieve optimum strata weights for better precision. In this study we attempt to analyze the behaviour of calibration estimators with different types of distance measures in the [...] Read more.
The calibration method is used in stratified random sampling in the presence of measurement error to achieve optimum strata weights for better precision. In this study we attempt to analyze the behaviour of calibration estimators with different types of distance measures in the presence of measurement error for the estimation of population mean under stratified random sampling. The proposed estimators are compared with the estimators in the absence of measurement error. A simulation study has been carried out to evaluate the proposed estimators. Full article
(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 2nd Edition)
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