Advances in Statistical Simulation and Computing

1. Introduction

In this Editorial, we are pleased to introduce the Special Issue of the journal Axioms entitled “Advances in Statistical Simulation and Computing”.

Statistical simulation and computational methods play a central role in addressing complex problems across a wide range of scientific disciplines. Simulation-based techniques, particularly those relying on stochastic sampling, provide indispensable tools for exploring probabilistic and statistical models that are analytically intractable. At the same time, the rapid growth in computational power and the development of advanced algorithms have significantly reduced computational costs, enabling more sophisticated analyses and large-scale studies.

The aim of this Special Issue is to bring together recent theoretical and applied contributions that advance simulation methodologies, computational techniques, and their applications in statistics and related fields. The published articles address novel probability models, robust and flexible inferential methods, efficient algorithms for large and complex datasets, and simulation-based assessments of statistical procedures. Collectively, these contributions reflect current trends and future directions in statistical simulation and computing.

2. Overview of the Published Papers

This Special Issue comprises eight peer-reviewed contributions, each addressing methodological, computational, or applied challenges in modern statistical simulation and computing.

In Contribution 1, Caamaño-Carrillo, Bevilacqua, Zamudio-Monserratt, and Contreras-Reyes develop a novel bivariate distribution constructed via the Appell hypergeometric function, with Pareto–Feller marginals derived from independent gamma random variables. The proposed model extends classical bivariate beta-type distributions and accommodates heavy-tailed behavior, a key feature in many applied settings. The authors provide a comprehensive analytical treatment, deriving distributional functions, moment-based characteristics, and information-theoretic measures, and they support their theoretical results with numerical illustrations.

In Contribution 2, Chocotea-Poca, Nicolis, and Ibacache-Pulgar focus on flexible modeling of binomial response data through the introduction of a skew–t link function. By incorporating both asymmetry and heavy tails, the proposed model enhances robustness and adaptability in regression settings characterized by complex data structures. A penalized likelihood estimation strategy is adopted to stabilize inference, and extensive simulation studies, together with real-data applications, demonstrate clear improvements over traditional symmetric and skewed link models.

In Contribution 3, Novoa-Muñoz and Aguirre-González address a long-standing gap in goodness-of-fit assessment for the bivariate negative binomial distribution. They propose a computationally efficient test based on a Cramér–von Mises-type statistic, combined with a reparameterization via the probability generating function. The null distribution is approximated using a parametric bootstrap scheme accelerated through parallel computing. Simulation results confirm accurate size control and satisfactory power, while real-data applications highlight the practical feasibility of the proposed approach.

In Contribution 4, Liu, Zhao, Xu, and Wang examine nonparametric specification testing for nonlinear regression models in the context of large-scale data. To overcome computational limitations, the authors employ a divide-and-conquer strategy and study the role of smoothing parameter selection in ensuring optimal test performance. By adopting a penalty-based method, they obtain a scalable test with an asymptotic normal null distribution and adaptive properties, as confirmed through numerical simulations.

In Contribution 5, Reyes, Arnold, Gómez, Venegas, and Gómez propose a new family of distributions designed to model non-negative bimodal data with an excess of small values. The model is constructed by modifying the exponential distribution through a polynomial adjustment, yielding greater flexibility in capturing complex distributional shapes. The authors investigate analytical properties, perform simulation-based maximum likelihood estimation, and demonstrate superior empirical performance in real-data applications when compared to existing bimodal exponential models.

In Contribution 6, Almulhim, Alamari, Laksaci, and Kaid introduce a nonparametric estimator for conditional mode estimation with functional covariates. The proposed method combines local linear smoothing with L1-robust techniques and formulates modal regression through the minimization of a quantile derivative. Theoretical results establish almost complete consistency and convergence rates consistent with those found in functional data analysis. Simulation experiments and real-data studies illustrate the estimator’s effectiveness in high-dimensional prediction contexts.

In Contribution 7, Jiang, Chen, and Yan develop a robust adaptive lasso methodology for autoregressive models, motivated by the need for robustness and sparsity in the presence of outliers and heavy-tailed innovations. By leveraging partial autocorrelation coefficients as adaptive penalty weights and a robust autocorrelation estimator based on the FQn statistic, the proposed approach improves parameter estimation and variable selection. Its performance is supported by simulation studies and applications to real datasets.

Finally, Contribution 8 by Phoophiwfa, Busababodhin, Volodin, and Suraphee presents a closed-form expression for the asymptotic variance of the coefficient of variation estimator under a reparameterized Birnbaum–Saunders distribution. Using moment-based estimation and the delta method, the authors derive compact analytical results that facilitate practical implementation. Monte Carlo simulations confirm favorable finite-sample properties, and an application to environmental data illustrates the relevance of the proposed methodology in applied statistical analysis.

3. Concluding Remarks

The contributions collected in this Special Issue reflect the growing importance of statistical simulation and computationally driven methodologies in modern statistical research. Across diverse contexts—ranging from distribution theory and regression modeling to time series analysis and functional data—the published papers emphasize robustness, computational efficiency, and practical applicability. Together, they illustrate how simulation-based approaches and advanced computational strategies can effectively address complex data structures and emerging challenges. We hope that this Special Issue will stimulate further methodological developments and foster continued research at the intersection of statistics, simulation, and computing.