The Austrian Journal of Statistics is an open-access journal (without any fees) including a long history. It is published approximately quarterly by the Austrian Statistical Society. Its general objective is to promote and extend the use of statistical methods in all kind of theoretical and applied disciplines. Special emphasis is on methods and results in official statistics. The Austrian Journal of Statistics is indexed in many data bases, such as Scopus (by Elsevier), Web of Science - ESCI by Clarivate Analytics (formely Thompson & Reuters), DOAJ, Scimago, and many more. Original papers and review articles in English will be published in the Austrian Journal of Statistics if judged consistently with these general aims. All papers will be refereed. Special topics sections will appear from time to time. Each section will have as a theme a specialized area of statistical application, theory, or methodology. Technical notes or problems for considerations under Shorter Communications are also invited. A special section is reserved for book reviews. The current estimated impact factor (via Publish or Perish) is 0.775, see HERE, or even more indices HERE. We are indexed in Scopus - the Austrian Journal of Statistics is indexed and listed in Scopus, DOAJ, Scimago and many other indices. Austrian Journal of Statistics ISNN number is 1026597X
The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.
Estimating the Mean of Finite Population under Double Sampling Stratification in the Presence of Non-Response
Estimating finite population mean is the primary concern in many studies, particulary when the non response occurs for some units. This study focuses in estimating the finite population mean using the auxiliary variables under double sampling stratification (DSS) in the presence of non-response which occurs on both the study and the auxiliary variables. A Regression-ratio-in-ratio type exponential strategy is proposed with non-response simultaneously. Expressions for bias and mean square errors (MSE) are derived up-to-first order of approximation. MSE and percentage relative efficiency (PRE) are computed numerically using vrious real data sets. A simulation study is also conducted to verify the performance of estimators. Results indicate that the proposed estimator has the minimum MSE and the maximum PRE compared to competitor estimators. Therefore the proposed estimator is more efficient and is recommended for practical use in future.
Copyright (c) 2025 Syed Muhammad Arsalan, Javid Shabbir, Alamgir Khalil https://creativecommons.org/licenses/by/3.0/
Log-Free Distance and Covariance Matrix for Compositional Data II: The Projective/Exterior Product Approach
Motivated by finding a way to deal with Compositional Data (CoDa) with or without zeroes in a unified way, we build upon the previous projective geometry viewpoint of Faugeras (2023) and use the tools provided by the exterior product and Grassmann’s algebra. These allow to represent higher dimensional subspaces as linear objects, called multi-vectors, on which the usual Euclidean scalar product can be extended. Applied to CoDa seen as equivalence classes, this allows to define a pseudo-scalar product and pseudo-norm. Depending on the normalization chosen, it is remarkable that the pseudo-norm obtained is either the same barycentric divergence which was derived in Faugeras(2024a) from the affine geometry viewpoint, or becomes a new, orthogonally invariant, genuine distance on the full non-negative CoDa space. These tools are then used to lay the foundations for further statistical analysis of CoDa: we show how the relative position of a pair of CoDa around their means can be decomposed along its components to form exterior covariance, variance and correlation matrices, along with their corresponding global scalar measure of (co)variation. Gaussian distributions, Mahalanobis distance, Fréchet means, etc.. can then be introduced and we sketch their potential statistical applications. Eventually, we establish some connections with various notions encountered in the literature, like divergences based on quantifying inequalities, or canonical angles between subspaces. The paper is preceded by a tutorial on the exterior product, based on intuitive geometric visualization and familiar linear algebra, in order to make the ideas of the paper accessible to non-specialists.
Copyright (c) 2025 Olivier Faugeras https://creativecommons.org/licenses/by/3.0/
Court Surfaces: A Compositional Approach to Tennis Analytics
Compositional data analysis (CoDA) has been extensively applied in fields such as microbiomics, geosciences, and health sciences, yet its potential in sports analytics remains largely untapped. This study applies CoDA to analyze the proportional distribution of matches played on different tennis court surfaces —clay, hard, and grass— and its influence on player rankings and performance. Data from 1,171 Association of Tennis Professionals (ATP) players ranked in the top 100 were examined, revealing significant differences in surface composition across ranking categories (p < 0.001). High-ranked players dedicated 57.8% of their total minutes to hard courts, compared to 32.6% on clay and 9.6% on grass, while lower-ranked players showed a lower proportion of tournaments on hard and a higher proportion on grass. Temporal trends indicated a shift from clay dominance in earlier decades to a predominance of hard courts, with players from the 2010s dedicating 59.8% of their tournament play to hard surfaces. These findings underscore the potential of CoDA to uncover nuanced relationships in sports data, providing actionable insights for optimizing strategies in tennis performance.
Special Issue on Compositional Data Analysis and CoDaWork 2024
Copyright (c) 2025 Pepus Daunis-i-Estadella, Ernest Baiget, Martí Casals https://creativecommons.org/licenses/by/3.0/
Simultaneous Inference in Finite Mixtures of Regression Models
A general framework for simultaneous inference in finite mixtures of generalized linear regression models is presented. Assuming asymptotic normality of the maximum likelihood estimate of all interesting model parameters, confidence regions and p-values using a maximum norm for the multivariate t-statistic are derived. This allows to simultaneously test all regression coefficients whether they are zero. Another application is to test for constant effects across mixture components. Size and power of the new methods are evaluated using artificial data. A real world data set on the productivity of PhD students is used to demonstrate the application of the procedures.
Special Issue. In memorial: Fritz Leisch
Copyright (c) 2025 Friedrich Leisch, Torsten Hothorn https://creativecommons.org/licenses/by/3.0/
Exploring Process Heterogeneity in Environmental Statistics: Examples and Methodological Advances
Environmental models typically rely on stationarity assumptions. However, environmental systems are complex, and processes change over states or seasons, leading to often overlooked heterogeneity. This paper explores methods to incorporate process heterogeneity into statistical models to improve their performance. It considers problems from natural hazards and earth system sciences, demonstrating the effects of process heterogeneity and proposing methodological advances through model extensions. The first problem addresses flood frequency analysis, where floods are generated by different processes in catchment and atmosphere. A mixture model combining peak-over-threshold distributions of flood types can handle this heterogeneity, especially regarding tail heaviness, making it relevant for flood design. The second problem involves minimum flow frequency analysis, with heterogeneity from different summer and winter processes. A mixture distribution model for minima and a copula-based estimator can incorporate seasonal distributions and event dependence, showing significant performance gains for extreme events. The third problem examines process heterogeneity in rainfall models. Clustering event characteristics (e.g., duration, intensity) using Gower's distance and a lightning index helps distinguish between convective and stratiform events, showing potential to enhance rainfall generators. The fourth problem deals with parameter variation in temporal models of environmental variables, using daily streamflow series. A tree-based machine learning model shows that prediction performance and model parameters vary with quantile loss optimization, suggesting the need for different or combined models for full time series in the presence of process heterogeneity. The study highlights the importance of considering process heterogeneity in modeling from the outset and encourages a better understanding of statistical assumptions and the enrichment of physical knowledge in environmental statistics.
Copyright (c) 2025 Gregor Laaha, Johannes Laimighofer, Nur Banu Özcelik, Svenja Fischer https://creativecommons.org/licenses/by/3.0/
Nonparametric Relative Error Regression for LTRC Data
In the present work, we propose a new kernel estimator of the regression function based on the minimization of the mean squared relative error, when the response variable is subject to both random left truncation and right censoring (LTRC). Such variables typically appear in a medical or an engineering life test studies. Under classical conditions we establish the uniform consistency with a rate and the asymptotic normality for the estimator. The performance of the regression function estimator is evaluated on simulated data sets.
Copyright (c) 2025 Latifa Adjoudj, Siham Bey, Zohra Guessoum, Abdelkader Tatachak https://creativecommons.org/licenses/by/3.0/
circlus: An R Package for Circular and Spherical Clustering Using Poisson Kernel-Based and Spherical Cauchy Distributions
This paper introduces circlus, an R package designed for clustering circular and spherical data using Poisson kernel-based (PKB) distributions and spherical Cauchy distributions. The package leverages the general framework for Expectation-Maximization (EM) estimation implemented by package flexmix and provides model drivers for estimating PKB and spherical Cauchy distributions in the components. The drivers implement two approaches for the M-step. The first is a direct maximization approach implemented in C++ via Rcpp, while the second incorporates covariates by solving the M-step using neural networks with the torch package. The package is particularly suited for highdimensional clustering tasks, such as text embeddings on a spherical space, and supportsmodels both with and without covariates. As a case study, we apply circlus to cluster the abstracts of papers co-authored by Fritz Leisch and demonstrate the use with and without the inclusion of co-author count as a covariate.
Copyright (c) 2025 Lukas Sablica, Kurt Hornik, Bettina Grün https://creativecommons.org/licenses/by/3.0/
cellKey - An R Package to Perturb Statistical Tables
National statistical offices (NSIs) routinely publish aggregated data in the form of statistical tables. However, ensuring data privacy is a critical aspect of this process. Anonymization techniques must be applied to these tables to safeguard the privacy of individual data contributors and prevent unauthorized inference about specific units from the published outputs as often required by law. The R package cellKey offers a possible solution to this challenge by implementing a post-tabular perturbation method. This method modifies table cell values after aggregation, ensuring that sensitive information is adequately masked. It is versatile, suitable for both frequency tables and magnitude tables. A key feature of the cellKey package is its ability to maintain consistency across multiple tables that share identical cells. This ensures that anonymized data across different tables remains coherent while still protecting privacy. This approach makes the package especially useful for scenarios involving complex datasets with interrelated tables. The cellKey package is user-friendly and can empower NSIs and other data holders to publish statistical outputs that uphold both data utility and privacy, meeting the growing demands for secure and accessible data dissemination.
Copyright (c) 2025 Bernhard Meindl https://creativecommons.org/licenses/by/3.0/
On an Alternative to Discrete Pareto Model
Here we introduce a novel and versatile discrete distribution as an alternative to discrete Pareto distribution and derive some noteworthy distributional properties. The proposed distribution has some interesting characteristics, such as decreasing hazard rate, unimodality, overdispersion and infinite divisibility. Some characterizations are also obtained. We also consider different estimation procedures for estimating the model parameters, namely: the maximum likelihood, least squares, weighted least squares, Cramer-von Mises methods and compare them using a comprehensive simulation study. Lastly, to illustrate the practical utility of the proposed model, we analyze four real datasets.
Copyright (c) 2025 K Jayakumar, Jiji Jose https://creativecommons.org/licenses/by/3.0/
Demonstrating the Capabilities of the lionfish Software for Interactive Visualization of Market Segmentation Partitions
Market segmentation partitions multivariate data using some clustering algorithm, resulting in some number of homogeneous clusters of consumers for marketing purposes. Often this type of data has no clear cluster structure, that is, no separations or gaps between clusters of points exist, which is why this is considered partitioning rather than clustering. Understanding the differences between the clusters is typically done by examining single features. However, this can be inconclusive as multiple clusters might share similar characteristics on individual features and the market segmentation partition actually defines the clusters based on different linear constraints on the features. To understand what uniquely characterizes a cluster of customers, examining linear combinations of features may be helpful. This article introduces the R package lionfish that provides interactive and dynamic tools to facilitate the exploration and refining of market segmentations. The package integrates tour algorithms that use linear combinations of features to view high-dimensional data, from the tourr package, with Python-powered interactivity, allowing manual control, interactive selection, and multiple linked windows, to support revising the cluster memberships based on visual feedback. The focus is on the widely used k-means clustering algorithm, but the tools also support other algorithms. The utility of the software is demonstrated through three example analyses from the domain of market segmentation. The flexible, user-driven approach provided by package lionfish offers deeper insights into complex market behaviors, enabling more effective segmentation and enhancing strategic decision-making.
Copyright (c) 2025 Matthias Medl, Dianne Cook, Ursula Laa https://creativecommons.org/licenses/by/3.0/
Examining Exams Using Rasch Models and Assessment of Measurement Invariance
Many statisticians regularly teach large lecture courses on statistics, probability, or mathematics for students from other fields such as business and economics, social sciences, psychology, etc. The corresponding exams often use a multiple-choice or single-choice format and are typically evaluated and graded automatically, either by scanning printed exams or via online learning management systems. Although further examinations of these exams would be of interest, these are frequently not carried out. For example a measurement scale for the difficulty of the questions (or items) and the ability of the students (or subjects) could be established using psychometric item response theory (IRT) models. Moreover, based on such a model it could be assessed whether the exam is really fair for all participants or whether certain items are easier (or more difficult) for certain subgroups of students. Here, several recent methods for assessing measurement invariance and for detecting differential item functioning in the Rasch model are discussed and applied to results from a first-year mathematics exam with single-choice items. Several categorical, ordered, and numeric covariates like gender, prior experience, and prior mathematics knowledge are available to form potential subgroups with differential item functioning. Specifically, all analyses are demonstrated with a hands-on R tutorial using the psycho* family of R packages (psychotools, psychotree, psychomix) which provide a unified approach to estimating, visualizing, testing, mixing, and partitioning a range of psychometric models. The paper is dedicated to the memory of Fritz Leisch (1968--2024) and his contributions to various aspects of this work are highlighted.
Copyright (c) 2025 Achim Zeileis https://creativecommons.org/licenses/by/3.0/
Time-Varying Correlations between Selected Exchange Rates: A Robust DCC-GARCH Model Approach
Effective diversification of global portfolios and risk management depends to a large extent on the degree of correlation between the returns of financial assets. The Dynamic Conditional Correlation Generalized Autoregressive Conditional Heteroscediency (DCC-GARCH) model addresses the time-varying correlation and volatility among financial assets. The model has a two-step process whereby the volatility of each individual asset is first estimated using the univariate GARCH and the time-varying correlation between those assets is then captured using the DCC framework. Although the DCC-GARCH setup allows for the use of any univariate GARCH model for the variance of each financial asset, when constructing a DCC-GARCH model, most researchers typically use only one univariate GARCH model for all the returns of the financial asset. This study proposes a robust DCC-GARCH model in analyzing the dynamics of time-varying correlations of financial data in which the optimal univariate GARCH models (with the lowest information criteria) for each financial asset are used to build up the DCC-GARCH model. An empirical application of this model in analyzing the time-varying conditional correlation between four exchange rates shows an improvement in results (relative to the information criterion values) compared to the case where only one univariate GARCH model is used to construct the DCC-GARCH model. Standardized residuals in the quasi maximum likelihood estimation (QMLE) procedure for DCC-GARCH parameters, are typically assumed to follow a multivariate Gaussian distribution. One stylized fact of financial data returns is that the residuals are heavy-tailed. We consider the case where the standardized residuals follow a multivariate Gaussian, and the case where they follow either a multivariate Student's t-distribution or a multivariate Laplace distribution. Results show that a robust DCC-GARCH model performs better when the standardized residuals follow a multivariate Student's t-distribution.
Copyright (c) 2025 Bruno Dinga, Jimbo Henri Claver, Cletus Kwa Kum https://creativecommons.org/licenses/by/3.0/
On a Control Chart for Monitoring Rates and Proportions Based on the Standard Two-sided Power Distribution
This paper proposes a new control chart based on the two-parameter standard two-sided power distribution for monitoring rates and proportions, that is, when the quality characteristic of interest belongs to the unit interval (0,1). Control charts based on the well-known beta and Kumaraswamy distributions are usually considered to deal with this kind of data. The standard two-sided power distribution has many similarities to the beta and Kumaraswamy distributions and a number of advantages in terms of tractability. We evaluate and compare the performance of the new control chart with the beta and Kumaraswamy control charts through Monte Carlo simulation experiments. The simulation results reveal that the control chart based on the standard two-sided power distribution outperforms the beta and Kumaraswamy control charts in terms of run length analysis. An empirical application to a real data set is considered to illustrate the new control chart in practice, and comparisons with the two most traditional control charts for rates and proportions (beta and Kumaraswamy) are made.
Copyright (c) 2025 Artur Lemonte https://creativecommons.org/licenses/by/3.0/
Stochastic Restricted Modified Mixed Logistic Estimator
In this study, we introduce a new estimator named the Stochastic Restricted Modified Mixed Logistic Estimator (SRMMLE), which is specifically designed to handle multicollinearity within the framework of stochastic linear restrictions. Further, we enhance the SRMMLE by modifying its coefficients, resulting in four distinct variants: Stochastic Restricted Modified Mixed Logistic Estimator 1 (SRMMLE1), Stochastic Restricted Modified Mixed Logistic Estimator 2 (SRMMLE2), Stochastic Restricted Modified Mixed Logistic Estimator 3 (SRMMLE3), and Stochastic Restricted Modified Mixed Logistic Estimator 4 (SRMMLE4). Based on the mean square error matrix criterion, we establish conditions for the superiority of SRMMLE over existing estimators, such as the Stochastic Restricted Maximum Likelihood Estimator (SRMLE), Stochastic Restricted Ridge Maximum Likelihood Estimator (SRRMLE), Stochastic Restricted Logistic Liu Estimator (SRLLE), and Stochastic Restricted Mixed Liu-Type Estimator (SRMLTE). In the simulation study, we determined the scalar mean square error and the K-fold cross-validated balanced accuracy of the estimators. Further, we present an empirical study and a real data application illustrating the superior performance of the proposed estimator. In particular, the SRMMLE4 outperforms others in terms of scalar mean square error and balanced accuracy.
Copyright (c) 2025 Thayaparan Kayathiri, Manickavasagar Kayanan, Pushpakanthie Wijekoon https://creativecommons.org/licenses/by/3.0/
Optimal Variable Acceptance Sampling Plan under Progressive Type-II Censoring for the Mixture of Exponential-Rayleigh Distributions
Mixture distributions are widely utilized in various practical problems, such as clinical experiments and electronic component life testing. Despite this, the literature does not extensively cover acceptance sampling plans associated with these distributions. In this paper, variable acceptance sampling plans are designed for a mixture of exponential-Rayleigh distributions using partially accelerated life tests. Under progressive Type-II censoring scheme, the maximum likelihood estimators of the unknown parameters of the mixture distribution are derived for Arrhenius and linear life-stress relationships. Based on these relationships, optimal variable sampling plans are formulated. The plan parameters are determined by solving corresponding optimization problems. The study presents numerical findings, a comparative analysis, and sensitivity assessments. Finally, the practical applicability and relevance of the proposed acceptance sampling plans are demonstrated using real-world datasets. These datasets include breast cancer patients' records and failure lifetime data from communication transmitter-receivers in a commercial aircraft.
Copyright (c) 2025 A. M. Mathai, M. Kumar https://creativecommons.org/licenses/by/3.0/
We investigate suitable methods for clustering multivariate ordinal data assuming that the data are collected in surveys with item batteries on the same ordinal answer format and that respondents are to be grouped to characterize different answering patterns and tendencies. We consider heuristic partitioning methods and model-based methods which fit within the flex-scheme proposed by Fritz Leisch for clustering, in combination with different variants of scale handling (numerical coding, nominalization and respecting the ordinal scale). The performance of the methods to extract the true clustering structure is assessed in an illustrative simulation study using artificial data where the number of observations, the number of variables and the number of response levels as well as the difficulty of the clustering problem are systematically varied to highlight in which situations certain methods might be preferable. By extending the flex-scheme with new methods, which we provide in our R package flexord, we help pave the way for future research on ordinal data clustering with even more complex and diverse data-generating processes.
Copyright (c) 2025 Dominik Ernst, Lena Ortega Menjivar, Theresa Scharl, Bettina Grün https://creativecommons.org/licenses/by/3.0/
Robust Filtering for Linear State-space Models with Non-propagating Outliers Following a Mixture of Gaussian Distributions
The problem of recursive filtering in linear state-space models is considered. The solution to this problem is the classical Kalman filter which is optimal in the sense that it minimizes the variance of the estimated states, if the error processes of the state and observation equations are both Gaussian. However, the Kalman filter is well known to be sensitive to outliers, so robustness is an issue. Two approximate conditional-mean (ACM) type filters for vector-valued observations are proposed that generalize existing univariate filters of similar type to the multivariate case. These new ACM-type filters are compared by simulations in a multivariate setting with additive outliers to the classical Kalman filter and the robust least squares (rLS) filter, another approach robustifying the Kalman filter. Additionally, different settings of tuning parameters and their impact are investigated. The results of the simulation experiments show that in the presence of additive outliers the multivariate ACM-type filters not only outperform the classical Kalman filter, as expected, but they also outperform the rLS filter.
Copyright (c) 2025 Bernhard Spangl https://creativecommons.org/licenses/by/3.0/
Reproducibility of statistical simulations is crucial but proved being a challenge in its own right. Recently, lack of reproducibility of important simulation studies stimulated developments of reporting guidelines and specific protocols trying to improve on this situation. The problem, of course, is not new and issues regarding reproducibility of numerical results, for example statistical analyses or simulations, have long been known. Documented lack of progress regarding reproducibility in the past decade naturally leads to the question if problem awareness was not powerful enough to lead to improved reproducibility. As a benchmark case, I tried to reproduce a simulation study in a so far unpublished manuscript by Fritz Leisch and myself. The results show that, time and again, the devil is in the details and much self-discipline and extensive record-keeping and documentation are mission critical.
Copyright (c) 2025 Torsten Hothorn https://creativecommons.org/licenses/by/3.0/
Excess Mortality in Austria during the COVID-19 Pandemic
The impact of the COVID-19 pandemic on the mortality in Austria is investigated. A recent pre-pandemic generation life table is developed. Using this pre-pandemic life table, the expected number of deaths for the years 2020 to 2023 is derived. Comparing the expected number of deaths to the observed number of deaths during the pandemic years yields the excess mortality for Austria in the years 2020 to 2023. The Austrian life table can be adjusted to the Austrian federal states, yielding for each Austrian federal state the excess mortality for the pandemic years. The excess mortality varies substantially across federal states and during the pandemic years. The results are discussed against some state-specific health-related and economic quantities, yielding correlations of excess mortality with age, medical care, economic quantities, and COVID-19 related quantities.
Copyright (c) 2025 Matthias Reitzner https://creativecommons.org/licenses/by/3.0/
Contributions of Fritz Leisch to Vignettes and Reproducible Research
In this paper we review the contributions of Dr. Fritz Leisch to the areas of reproducible research and software documentation. We first review three emergent use cases for these contributions and then describe the computational tools and methods needed to support them. We then discuss some of the risks that exist for each of the use cases and consider developments that might help to mitigate those risks. And we end by considering how they may evolve in the coming years.
Copyright (c) 2025 Robert Gentleman, Anthony Rossini, Vincent Carey https://creativecommons.org/licenses/by/3.0/
E-Bayesian Estimation of Rayleigh Distribution and Its Evaluation Standards: E-posterior Risks and E-MSEs under Progressive Type-II Censoring
The present study considers the problem of estimating the scale parameter, reliability function, and hazard function of Rayleigh distribution using the E-Bayesian estimation approach when progressively Type-II censored data are available. The evaluation standards of these estimates are accessed through the definition of E-posterior risk (expected posterior risk) and E-MSE (expected mean square error). These estimations are carried out using conjugate prior distributions of the unknown parameters under four different loss functions i.e. quadratic, weighted squared error, Degroot, and entropy loss functions. Further, we perform Monte Carlo simulations to compare the performances of these proposed methods and use a real dataset for illustration purposes.
Copyright (c) 2025 Mahesh Kumar Panda, Lipsa Rani Bhoi https://creativecommons.org/licenses/by/3.0/
Inference on Partially Observed Competing Risks Models Using Generalized Type-II Hybrid Censoring Scheme
This article investigates inference in a competing risks model where failure causes are partially observed, assuming latent failure times follow Weibull distributions. Inference is derived under a generalized type-II hybrid censoring scheme. The maximum likelihood estimators for model parameters and their associated confidence intervals are discussed. Also, we compute Bayes estimators under both informative and non-informative priors, along with their credible intervals. The performance of all estimators is evaluated through Monte Carlo simulations. Finally, for illustrative purposes, a real-world case is explored.
Copyright (c) 2025 G. S. Deepthy, K. K. Anakha, Sebastian Nicy https://creativecommons.org/licenses/by/3.0/
Tooling for Reproducible Research: Considerations for the Past and Future of Data Analysis
The concept of reproducible research has evolved significantly over the past 30 years, with the idea growing in popularity, awareness, and acceptance. Upon its introduction to the statistical and broader scientific community, computational reproducibility was proposed as an essential concept for communicating the process of computational research and for being able to understand what exactly was done to produce a result. However, in the early stages, computational reproducibility faced at least one significant challenge, which was the lack of tools to make it easier for people to implement reproducible workflows. Fritz Leisch made major contributions to this area with his development of Sweave for the R programming language and his general promotion of software tools for reproducibility. We consider these contributions in the context of the history of reproducible research and consider what the implications are for the future of data analysis.
Copyright (c) 2025 Roger Peng https://creativecommons.org/licenses/by/3.0/
In this paper, we extend the Asmussen-Rosinski approach for the approximation of Levy processes. To simulate the value of the process at time t, we introduce a time-dependent truncation of the Levy measure, which we refer to as dynamic cutting, followed by the simulation of the large-jump component. We provide the sufficient condition under which the compensated small-jump part can be replaced by a Gaussian approximation. We also derive weak approximation rates for both approaches. Finally, we run numerical simulations and compare the performance of our method with the Asmussen-Rosinski approach.
Special Issue Department of Probability, Statistics and Actuarial Mathematics at TSNU of Kyiv
Copyright (c) 2025 Dmytro Ivanenko, Victoria Knopova, Denis Platonov https://creativecommons.org/licenses/by/3.0/
Statistical Estimation and Hypothesis Testing on Impulse Response Function
In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function (IRF) which is defined on a bounded domain. A sample input- output cross-correlogram is taken as an estimator of the response function. The input processes are supposed to be zero-mean stationary Gaussian process and can be repre- sented as a finite sum with uncorrelated terms. A rate of convergence of IRF estimator in the space L2([0,Λ]) is obtained that gives a possibility to propose a nonparametric goodness-of-fit testing on IRF.
Copyright (c) 2025 Iryna Rozora, Anastasiia Melnyk https://creativecommons.org/licenses/by/3.0/
Asymptotic Properties of Functionals of the Squared Periodograms for Stationary Random Fields
The paper presents conditions for the asymptotic normality of functionals of squared periodograms based on tapered data. Stationary Gaussian random fields are considered. Two limit theorems are stated: for the first one the certain condition of integrability of the spectral density of the field is assumed, and the second result is for spectral densities with the prescribed behavior near the points of singularities.
Copyright (c) 2025 Lyudmyla Sakhno https://creativecommons.org/licenses/by/3.0/
Student Models for a Risky Asset with Dependence: Option Pricing and Greeks
We propose several new models in finance known as the Fractal Activity Time Geometric Brownian Motion (FATGBM) models with Student marginals. We summarize four models that construct stochastic processes of underlying prices with short-range and long-range dependencies. We derive solutions of option Greeks and compare with those in the Black-Scholes model. We analyse performance of delta hedging strategy using simulated time series data and verify that hedging errors are biased particularly for long-range dependence cases. We also apply underlying model calibration on S&P 500 index (SPX) and the U.S./Euro rate, and implement delta hedging on SPX options.
Copyright (c) 2025 Nikolai Leonenko, Anqi Liu, Nataliya Schestyuk https://creativecommons.org/licenses/by/3.0/
On a Generalized Alpha Skew Laplace Distribution: Properties and Applications
This study introduces a novel extension of the alpha skew Laplace distribution (Harandi and Alamatsaz 2013), designed to model datasets with both unimodal and bimodal characteristics effectively. A detailed examination of its statistical properties is conducted, including moments, moment-generating functions, cumulative distribution functions, and characterization results based on conditional distributions. The study also develops a location-scale generalization, enhancing the scope of the distribution for broader applications. Besides, parameter estimation is performed using maximum likelihood methods, supported by a comprehensive analysis of the Fisher Information Matrix, ensuring robust and precise inference. The utility of the new distribution is validated through simulation studies which confirms the asymptotic consistency of its parameter estimates under varying sample sizes. Real-life applications involving white cell count data of Australian athletes and failure times of aircraft windshields demonstrate its superior performance over some established models. The newly introduced model consistently achieves lower Akaike and Bayesian Information Criteria (AIC/BIC) values, confirming its efficacy in fitting complex datasets. Additionally, likelihood ratio tests provide statistical evidence supporting its distinct advantages over nested models. This distribution represents a significant advancement in the field of probability and statistical modeling, offering a robust and versatile tool for analyzing diverse datasets with asymmetric or bimodal traits.
Copyright (c) 2025 Jondeep Das, Partha Jyoti Hazarika, Dimpal Pathak, Piotr Sulewski https://creativecommons.org/licenses/by/3.0/
Product Autoregressive Models: Review of Properties, Estimation Methods and Applications
Analysis of continuous non-negative time series data using multiplicative models is a growing area of research. When the variable of interest is non-negative, often some methodology based on transformation was followed in the literature. Even though a useful class of models known as product autoregressive models was appeared in the literature long back, the further advancements happened only in the last decade. Through subsequent developments, it was shown that the product form of an additive autoregressive model is preferable to its linear counterpart when non-negativity has to be taken care. This paper aims to provide an exhaustive review of theoretical and empirical works conducted on product autoregressive models in the context of non-linear and non-Gaussian time series modelling. The notable properties, estimation methods and applications of these models are discussed followed by a description of some possible future research avenues on this area.
Copyright (c) 2025 Rahul Thekkedath, Shiji Kavungal, Muhammed Anvar P https://creativecommons.org/licenses/by/3.0/
A New Regression Model Based on an Extended Inverse Gaussian Distribution with Application to Soybean Processing Plants in Brazil
Grain producers in Brazil often depend on third-party services for the transportation, processing and storage of their production, as, for the most part, they do not have silos on their properties. In this context, efficient logistics is essential to optimize processes and increase reliability between customers and service providers. This study focuses on the logistical analysis of truck traffic at two grain processing plants, examining different receiving protocols to evaluate internal vehicle flow during peak production conditions. The data is analyzed using a multiple regression model with two systematic components based on the proposed New Weibull inverse Gaussian distribution. The research is conducted in grain processing and storage units in the southwest region of São Paulo-SP, belonging to an agro-industrial cooperative. The study monitors all stages of soybean receipt during the peak harvest month, in March 2020. The results indicate the dependence of service times on the sector's logistical variables. This research addresses the pressing need for efficient logistics in the grain industry, especially in soybean processing. By focusing on truck traffic and receiving protocols, the study aims to provide a better understanding to optimize internal logistics processes, thus contributing to improving operational efficiency and customer service in grain processing units.
Copyright (c) 2025 Julio Cezar Souza Vasconcelos, Denize P. dos Santos, Pâmela Rafaela O.B. Cavallari, Edwin M.M. Ortega, Roberto Vila, Gauss M. Cordeiro, Marco Antônio M. Biaggioni https://creativecommons.org/licenses/by/3.0/