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Residuals are essential in regression analysis for evaluating model adequacy, validating assumptions, and detecting outliers or influential data. While traditional residuals perform well in linear regression, they face limitations in exponential family models, such as those based on the binomial and Poisson distributions, due to heteroscedasticity and dependence among observations. This article introduces a novel standardized combined residual for linear and nonlinear regression models within the exponential family. By integrating information from both the mean and dispersion sub-models, the new residual provides a unified diagnostic tool that enhances computational efficiency and eliminates the need for projection matrices. Simulation studies and real-world applications demonstrate its advantages in efficiency and interpretability over traditional residuals. [ABSTRACT FROM AUTHOR]

In applied and computational mathematics, quaternions are fundamental in representing three-dimensional rotations. However, specific types of quaternionic linear matrix equations remain few explored. This study introduces new quaternionic linear matrix equations and their necessary and sufficient conditions for solvability. We employ a methodology involving lemmas and ranks of coefficient matrices to develop a novel algorithm. This algorithm is validated through numerical examples, showing its applications in advanced fields. In control theory, these equations are used for analyzing control systems, particularly for spacecraft attitude control in aerospace engineering and for control of arms in robotics. In quantum computing, quaternionic equations model quantum gates and transformations, which are important for algorithms and error correction, contributing to the development of fault-tolerant quantum computers. In signal processing, these equations enhance multidimensional signal filtering and noise reduction, with applications in color image processing and radar signal analysis. We extend our study to include cases of η -Hermitian and i-Hermitian solutions. Our work represents an advancement in applied mathematics, providing computational methods for solving quaternionic matrix equations and expanding their practical applications. [ABSTRACT FROM AUTHOR]

This study evaluates the symmetry of data distributions after normalization, focusing on various statistical tests, including a few explored test named Rp. We apply normalization techniques, such as variance stabilizing transformations, to ribonucleic acid sequencing data with varying sample sizes to assess their effectiveness in achieving symmetric data distributions. Our findings reveal that while normalization generally induces symmetry, some samples retain asymmetric distributions, challenging the conventional assumption of post-normalization symmetry. The Rp test, in particular, shows superior performance when there are variations in sample size and data distribution, making it a preferred tool for assessing symmetry when applied to genomic data. This finding underscores the importance of validating symmetry assumptions during data normalization, especially in genomic data, as overlooked asymmetries can lead to potential inaccuracies in downstream analyses. We analyze postmortem lateral temporal lobe samples to explore normal aging and Alzheimer's disease, highlighting the critical role of symmetry testing in the accurate interpretation of genomic data. [ABSTRACT FROM AUTHOR]

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]

Understanding household energy-consumption patterns is essential for developing effective energy-conservation strategies. This study aims to identify 'out-profiled' consumers—households that exhibit atypical energy-usage behaviors—by applying four distinct feature-selection methodologies. Specifically, we utilized the chi-square independence test to assess feature independence, recursive feature elimination with multinomial logistic regression (RFE-MLR) to identify optimal feature subsets, random forest (RF) to determine feature importance, and a combined fuzzy rough feature selection with fuzzy rough nearest neighbors (FRFS-FRNN) for handling uncertainty and imprecision in data. These methods were applied to a dataset based on a survey of 383 households in Brazil, capturing various factors such as household size, income levels, geographical location, and appliance usage. Our analysis revealed that key features such as the number of people in the household, heating and air conditioning usage, and income levels significantly influence energy consumption. The novelty of our work lies in the comprehensive application of these advanced feature-selection techniques to identify atypical consumption patterns in a specific regional context. The results showed that households without heating and air conditioning equipment in medium- or high-consumption profiles, and those with lower- or medium-income levels in medium- or high-consumption profiles, were considered out-profiled. These findings provide actionable insights for energy providers and policymakers, enabling the design of targeted energy-conservation strategies. This study demonstrates the importance of tailored approaches in promoting sustainable energy consumption and highlights notable deviations in energy-use patterns, offering a foundation for future research and policy development. [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]

In this article, we present a novel methodology for inventory management in the pharmaceutical industry, considering the nature of its supply chain. Traditional inventory models often fail to capture the particularities of the pharmaceutical sector, characterized by limited storage space, product degradation, and trade credits. To address these particularities, using fuzzy logic, we propose models that are adaptable to real-world scenarios. The proposed models are designed to reduce total costs for both vendors and clients, a gap not explored in the existing literature. Our methodology employs pentagonal fuzzy number (PFN) arithmetic and Kuhn–Tucker optimization. Additionally, the integration of the naive Bayes (NB) classifier and the use of the Weka artificial intelligence suite increase the effectiveness of our model in complex decision-making environments. A key finding is the high classification accuracy of the model, with the NB classifier correctly categorizing approximately 95.9% of the scenarios, indicating an operational efficiency. This finding is complemented by the model capability to determine the optimal production quantity, considering cost factors related to manufacturing and transportation, which is essential in minimizing overall inventory costs. Our methodology, based on machine learning and fuzzy logic, enhances the inventory management in dynamic sectors like the pharmaceutical industry. While our focus is on a single-product scenario between suppliers and buyers, future research hopes to extend this focus to wider contexts, as epidemic conditions and other applications. [ABSTRACT FROM AUTHOR]