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The modeling of data involving proportions, confined to a unit interval, is crucial in diverse research fields. Such data, expressing part-to-whole relationships, span from the proportion of individuals affected by diseases to the allocation of resources in economic sectors and the survival rates of species in ecology. However, modeling these data and interpreting information obtained from them present challenges, particularly when there is high zero–one inflation at the extremes of the unit interval, which indicates the complete absence or full occurrence of a characteristic or event. This inflation limits traditional statistical models, which often fail to capture the underlying distribution, leading to biased or imprecise statistical inferences. To address these challenges, we propose and derive the skew-normal zero–one inflated (SNZOI) models, a novel class of asymmetric regression models specifically designed to accommodate zero–one inflation presented in the data. By integrating a continuous-discrete mixture distribution with covariates in both continuous and discrete parts, SNZOI models exhibit superior capability compared to traditional models when describing these complex data structures. The applicability and effectiveness of the proposed models are demonstrated through case studies, including the analysis of medical data. Precise modeling of inflated proportion data unveils insights representing advancements in the statistical analysis of such studies. The present investigation highlights the limitations of existing models and shows the potential of SNZOI models to provide more accurate and precise inferences in the presence of zero–one inflation. [ABSTRACT FROM AUTHOR]

This article explores Sylvester quaternion matrix equations and potential applications, which are important in fields such as control theory, graphics, sensitivity analysis, and threedimensional rotations. Recognizing that the determination of solutions and computational methods for these equations is evolving, our study contributes to the area by establishing solvability conditions and providing explicit solution formulations using generalized inverses. We also introduce an algorithm that utilizes representations of quaternion Moore-Penrose inverses to improve computational efficiency. This algorithm is validated with a numerical example, demonstrating its practical utility. Additionally, our findings offer a generalized framework in which various existing results in the area can be viewed as specific instances, showing the breadth and applicability of our approach. Acknowledging the challenges in handling large systems, we propose future research focused on further improving algorithmic efficiency and expanding the applications to diverse algebraic structures. Overall, our research establishes the theoretical foundations necessary for solving Sylvester-type quaternion matrix equations and introduces a novel algorithmic solution to address their computational challenges, enhancing both the theoretical understanding and practical implementation of these complex equations. [ABSTRACT FROM AUTHOR]

Developing efficient energy conservation and strategies is relevant in the context of climate change and rising energy demands. The objective of this study is to model and predict the electrical power consumption patterns in Brazilian households, considering the thresholds for energy use. Our methodology utilizes advanced machine learning methods, such as agglomerative hierarchical clustering, k-means clustering, and self-organizing maps, to identify such patterns. Gradient boosting, chosen for its robustness and accuracy, is used as a benchmark to evaluate the performance of these methods. Our methodology reveals consumption patterns from the perspectives of both users and energy providers, assessing the corresponding effectiveness according to stakeholder needs. Consequently, the methodology provides a comprehensive empirical framework that supports strategic decision making in the management of energy consumption. Our findings demonstrate that k-means clustering outperforms other methods, offering a more precise classification of consumption patterns. This finding aids in the development of targeted energy policies and enhances resource management strategies. The present research shows the applicability of advanced analytical methods in specific contexts, showing their potential to shape future energy policies and practices. [ABSTRACT FROM AUTHOR]

This study comprehensively explores the research landscape within statistical and reliability studies, focusing on the Birnbaum-Saunders distribution, Gaussian inverse distribution, cumulative damage models, and fatigue life prediction. Using a combination of bibliometric analysis, network visualization, thematic mapping, and latent Dirichlet allocation, we analyze 465 articles from the ISI Web of Science database. These articles were selected for their relevance based on a targeted search strategy. Our analysis identifies key trends, collaboration networks, and emerging research themes. Notable growth in scholarly activity was observed from 2015 to 2021, with a peak around 2021, followed by a decline in the number of publications. Relevant contributions were noted from countries such as Brazil, Canada, Chile, China, Iran, Japan, and the United States. The thematic analysis of keywords reveals influential motor themes like the Birnbaum-Saunders distribution and expectation-maximization algorithm; specialized niche areas such as producer risk; emerging or declining themes like the generalized Birnbaum-Saunders distribution; and foundational themes including cumulative damage and fatigue life distributions. A cluster analysis states key focus areas, such as material durability and advanced statistical methods. Integrating latent Dirichlet allocation, six main topics are derived, capturing broad thematic structures. However, some niche areas do not align directly due to their specialized nature and limited cross-field impact. These findings map the current research on this thematic and suggest future research directions, including deeper exploration of niche themes, integration of advanced statistical methods in practical applications, and increased collaboration across diverse research areas to enhance the robustness and applicability of reliability models. [ABSTRACT FROM AUTHOR]

Autoregressive models in time series are useful in various areas. In this article, we propose a skew-t autoregressive model. We estimate its parameters using the expectation-maximization (EM) method and develop the influence methodology based on local perturbations for its validation. We obtain the normal curvatures for four perturbation strategies to identify influential observations, and then to assess their performance through Monte Carlo simulations. An example of financial data analysis is presented to study daily log-returns for Brent crude futures and investigate possible impact by the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]