Axioms

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Open AccessEditorial

Advances in Statistical Simulation and Computing

by Francisco Novoa-Muñoz and Bernardo M. Lagos-Álvarez

Axioms 2026, 15(1), 62; https://doi.org/10.3390/axioms15010062 - 16 Jan 2026

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Abstract

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

(This article belongs to the Special Issue Advances in Statistical Simulation and Computing)

Research

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16 pages, 2118 KB

Open AccessArticle

Derivation of a Closed-Form Asymptotic Variance for the Coefficient of Variation Under the Reparameterized Birnbaum–Saunders Distribution

by Tossapol Phoophiwfa, Piyapatr Busababodhin, Andrei Volodin and Sujitta Suraphee

Axioms 2025, 14(11), 792; https://doi.org/10.3390/axioms14110792 - 28 Oct 2025

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Abstract

This study develops a tractable, closed-form expression for the asymptotic variance of the coefficient of variation (CV) estimator under a reparameterized Birnbaum–Saunders (BirSau) distribution. Using the method of moments, we derive analytical formulas for the mean, variance, and coefficient of variation of [...] Read more.

This study develops a tractable, closed-form expression for the asymptotic variance of the coefficient of variation (CV) estimator under a reparameterized Birnbaum–Saunders (BirSau) distribution. Using the method of moments, we derive analytical formulas for the mean, variance, and coefficient of variation of

X \sim BirSau (μ, λ)

and construct a plug-in estimator for the CV. By applying the delta method within this new nonlinear parametrization, we obtain an explicit and compact expression for the asymptotic variance of the CV estimator, thereby extending general asymptotic theory to a distribution-specific setting where higher-order moments lack closed forms under the classical parametrization. Extensive Monte Carlo simulations are conducted to examine the estimator’s finite-sample performance under various parameter configurations and sample sizes. The results demonstrate that the estimator exhibits decreasing bias and variance as the sample size increases, with strong convergence to its theoretical asymptotic behavior. A real-data application using rainfall measurements from northeastern Thailand further illustrates the practical utility of the proposed approach in quantifying relative variability across regions. These findings provide a concise analytical foundation for the coefficient of variation under the Birnbaum–Saunders framework, enhancing its theoretical development and facilitating practical implementation in environmental and reliability analyses. Full article

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15 pages, 341 KB

Open AccessArticle

Robust Adaptive Lasso via Robust Sample Autocorrelation Coefficient for the Autoregressive Models

by Yunlu Jiang, Fudong Chen and Xiao Yan

Axioms 2025, 14(9), 701; https://doi.org/10.3390/axioms14090701 - 17 Sep 2025

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Abstract

For the autoregressive models, classical estimation methods, including the least squares estimator or the maximum likelihood estimator are not robust to heavy-tailed distributions or outliers in the dataset, and lack sparsity, leading to potentially inaccurate estimation and poor generalization capability. Meanwhile, the existing [...] Read more.

For the autoregressive models, classical estimation methods, including the least squares estimator or the maximum likelihood estimator are not robust to heavy-tailed distributions or outliers in the dataset, and lack sparsity, leading to potentially inaccurate estimation and poor generalization capability. Meanwhile, the existing variable selection methods can not handle the case where the influence of explanatory variables on the dependent variable gradually weakens as the lag order increases. To address these issues, we propose a novel robust adaptive lasso method for the autoregressive models. The proposed method is constructed by using partial autocorrelation coefficients as adaptive penalty weights to promote sparsity in parameter estimation, and by employing a robust autocorrelation estimator based on the

F Q_{n}

statistic to enhance resistance to outliers. Numerical simulations and two real data analyses illustrate the promising performance of our proposed approach. The results indicate that our proposed approach exhibits good robustness and sparsity in the presence of outliers in the dataset. Full article

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21 pages, 962 KB

Open AccessArticle

Modal Regression Estimation by Local Linear Approach in High-Dimensional Data Case

by Fatimah A. Almulhim, Mohammed B. Alamari, Ali Laksaci and Zoulikha Kaid

Axioms 2025, 14(7), 537; https://doi.org/10.3390/axioms14070537 - 16 Jul 2025

Cited by 2 | Viewed by 904

Abstract

This paper introduces a new nonparametric estimator for detecting the conditional mode in the functional input variable setting. The estimator integrates a local linear approach with an

L^{1}

-robust algorithm and treats the modal regression as the minimizer of the quantile derivative. [...] Read more.

This paper introduces a new nonparametric estimator for detecting the conditional mode in the functional input variable setting. The estimator integrates a local linear approach with an

L^{1}

-robust algorithm and treats the modal regression as the minimizer of the quantile derivative. As an asymptotic result, we derive the theoretical properties of the estimator by analyzing its convergence rate under the almost complete consistency framework. The result is stated under standard conditions, characterizing both the functional structure of the data and the local linear approximation properties of the model. Moreover, the expression of the convergence rate retains the usual form of the stochastic convergence rate in functional statistics. Simulations and real-data applications demonstrate the algorithm’s effectiveness, showing its advantage over existing methods in high-dimensional prediction tasks. Full article

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18 pages, 695 KB

Open AccessArticle

Modified Bimodal Exponential Distribution with Applications

by Jimmy Reyes, Barry C. Arnold, Yolanda M. Gómez, Osvaldo Venegas and Héctor W. Gómez

Axioms 2025, 14(6), 461; https://doi.org/10.3390/axioms14060461 - 12 Jun 2025

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Abstract

In this paper, we introduce a new distribution for modeling bimodal data supported on non-negative real numbers and particularly suited with an excess of very small values. This family of distributions is derived by multiplying the exponential distribution by a fourth-degree polynomial, resulting [...] Read more.

In this paper, we introduce a new distribution for modeling bimodal data supported on non-negative real numbers and particularly suited with an excess of very small values. This family of distributions is derived by multiplying the exponential distribution by a fourth-degree polynomial, resulting in a model that better fits the shape of the second mode of the empirical distribution of the data. We study the general density of this new family of distributions, along with its properties, moments, and skewness and kurtosis coefficients. A simulation study is performed to estimate parameters by the maximum likelihood method. Additionally, we present two applications to real-world datasets, demonstrating that the new distribution provides a better fit than the bimodal exponential distribution. Full article

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15 pages, 694 KB

Open AccessArticle

Optimal Minimax Rate of Smoothing Parameter in Distributed Nonparametric Specification Test

by Peili Liu, Yanyan Zhao, Libai Xu and Tao Wang

Axioms 2025, 14(3), 228; https://doi.org/10.3390/axioms14030228 - 19 Mar 2025

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Abstract

A model specification test is a statistical procedure used to assess whether a given statistical model accurately represents the underlying data-generating process. The smoothing-based nonparametric specification test is widely used due to its efficiency against “singular” local alternatives. However, large modern datasets create [...] Read more.

A model specification test is a statistical procedure used to assess whether a given statistical model accurately represents the underlying data-generating process. The smoothing-based nonparametric specification test is widely used due to its efficiency against “singular” local alternatives. However, large modern datasets create various computational problems when implementing the nonparametric specification test. The divide-and-conquer algorithm is highly effective for handling large datasets, as it can break down a large dataset into more manageable datasets. By applying divide-and-conquer, the nonparametric specification test can handle the computational problems induced by the massive size of the modern datasets, leading to improved scalability and efficiency and reduced processing time. However, the selection of smoothing parameters for optimal power of the distributed algorithm is an important problem. The rate of the smoothing parameter that ensures rate optimality of the test in the context of testing the specification of a nonlinear parametric regression function is studied in the literature. In this paper, we verified the uniqueness of the rate of the smoothing parameter that ensures the rate optimality of divide-and-conquer-based tests. By employing a penalty method to select the smoothing parameter, we obtain a test with an asymptotic normal null distribution and adaptiveness properties. The performance of this test is further illustrated through numerical simulations. Full article

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30 pages, 775 KB

Open AccessArticle

Goodness-of-Fit Test for the Bivariate Negative Binomial Distribution

by Francisco Novoa-Muñoz and Juan Pablo Aguirre-González

Axioms 2025, 14(1), 54; https://doi.org/10.3390/axioms14010054 - 12 Jan 2025

Viewed by 1440

Abstract

When modeling real-world data, we face the challenge of determining which probability distribution best represents the data. To address this intricate problem, we rely on goodness-of-fit tests. However, when the data come from a bivariate negative binomial distribution, the literature reveals no existing [...] Read more.

When modeling real-world data, we face the challenge of determining which probability distribution best represents the data. To address this intricate problem, we rely on goodness-of-fit tests. However, when the data come from a bivariate negative binomial distribution, the literature reveals no existing goodness-of-fit test for this distribution. For this reason, in this article, we propose and study a computationally convenient goodness-of-fit test for the bivariate negative binomial distribution. This test is based on a bootstrap approximation and a parallelization strategy. To this end, we use a reparameterization technique based on the probability generating function and a Cramér-von Mises-type statistic. From the simulation studies, we conclude that the results converge to the established nominal levels as the sample size increases, and in all cases considered, the parametric bootstrap method provides an accurate approximation of the null distribution of the statistic we propose. Additionally, we verify the power of the proposed test, as well as its application to five real datasets. To accelerate the massive computational work, we employ the parallelization strategy that, according to Novoa-Muñoz (2024), was the most efficient among the techniques he analyzed. Full article

(This article belongs to the Special Issue Advances in Statistical Simulation and Computing)

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19 pages, 1058 KB

Open AccessArticle

Maximum Penalized Likelihood Estimation of the Skew–t Link Model for Binomial Response Data

by Omar Chocotea-Poca, Orietta Nicolis and Germán Ibacache-Pulgar

Axioms 2024, 13(11), 749; https://doi.org/10.3390/axioms13110749 - 30 Oct 2024

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Abstract

A critical aspect of modeling binomial response data is selecting an appropriate link function, as an improper choice can significantly affect model precision. This paper introduces the skew–t link model, an extension of the skew–probit model, offering increased flexibility by incorporating both [...] Read more.

A critical aspect of modeling binomial response data is selecting an appropriate link function, as an improper choice can significantly affect model precision. This paper introduces the skew–t link model, an extension of the skew–probit model, offering increased flexibility by incorporating both asymmetry and heavy tails, making it suitable for asymmetric and complex data structures. A penalized likelihood-based estimation method is proposed to stabilize parameter estimation, particularly for the asymmetry parameter. Extensive simulation studies demonstrate the model’s superior performance in terms of lower bias, root mean squared error (RMSE), and robustness compared to traditional symmetric models like probit and logit. Furthermore, the model is applied to two real-world datasets: one concerning women’s labor participation and another related to cardiovascular disease outcomes, both showing superior fitting capabilities compared to more traditional models (with probit and the skew–probit links). These findings highlight the model’s applicability to socioeconomic and medical research, characterized by skew and asymmetric data. Moreover, the proposed model could be applied in various domains where data exhibit asymmetry and complex structures. Full article

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17 pages, 892 KB

Open AccessArticle

Bivariate Pareto–Feller Distribution Based on Appell Hypergeometric Function

by Christian Caamaño-Carrillo, Moreno Bevilacqua, Michael Zamudio-Monserratt and Javier E. Contreras-Reyes

Axioms 2024, 13(10), 701; https://doi.org/10.3390/axioms13100701 - 9 Oct 2024

Cited by 1 | Viewed by 1707

Abstract

The Pareto–Feller distribution has been widely used across various disciplines to model “heavy-tailed” phenomena, where extreme events such as high incomes or large losses are of interest. In this paper, we present a new bivariate distribution based on the Appell hypergeometric function with [...] Read more.

The Pareto–Feller distribution has been widely used across various disciplines to model “heavy-tailed” phenomena, where extreme events such as high incomes or large losses are of interest. In this paper, we present a new bivariate distribution based on the Appell hypergeometric function with marginal Pareto–Feller distributions obtained from two independent gamma random variables. The proposed distribution has the beta prime marginal distributions as special case, which were obtained using a Kibble-type bivariate gamma distribution, and the stochastic representation was obtained by the quotient of a scale mixture of two gamma random variables. This result can be viewed as a generalization of the standard bivariate beta I (or inverted bivariate beta distribution). Moreover, the obtained bivariate density is based on two confluent hypergeometric functions. Then, we derive the probability distribution function, the cumulative distribution function, the moment-generating function, the characteristic function, the approximated differential entropy, and the approximated mutual information index. Based on numerical examples, the exact and approximated expressions are shown. Full article

(This article belongs to the Special Issue Advances in Statistical Simulation and Computing)

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