Advances in Distribution Theory: Extreme Values, Heavy-Tailed and Skewed Models, and Machine Learning Integration

In probability and statistics, the modelling of complex phenomena necessitates sophisticated distributional frameworks that extend beyond classical families such as the normal or exponential. Increasingly, data from finance, climate science, epidemiology, biomedical research, insurance, and other high-frequency domains reveal characteristics such as heavy tails, skewness, intricate dependence, tail dependence, and the presence of rare yet consequential extremes. Standard distributions often fall short in capturing these features, particularly in the face of asymmetry, volatility clustering, and multivariate dependencies. Recent literature demonstrates rapid progress in the development of new parametric and semi-parametric distributions, copula theory, and extreme value models. However, integrating these theoretical advances with robust inference and practical applications—especially where modern machine learning meets probability theory—remains an open frontier. There is also a noted lack of rigorous theoretical guarantees for many flexible machine learning tools when applied to heavy-tailed or extreme-valued data, leaving questions regarding tail behaviour, existence of moments, and asymptotic properties unresolved. This Research Topic aims to catalyse both theoretical and applied developments in modern distribution theory, emphasizing extreme value modelling, heavy-tailed and skewed distributions, and the integration of recent machine learning methodologies for density construction and inference. We seek to bridge conventional probability models with emerging computational and neural approaches, fostering new insights into modelling skewness, extremal behaviour, and complex multivariate dependence. Key questions include: how to best construct and infer flexible distributions for highly non-Gaussian data, how to rigorously describe and estimate tail-related quantities, and what principles ensure the reliability of machine learning techniques in these contexts. The scope of this Research Topic encompasses both foundational and methodological contributions, as well as computational and applied studies relevant to modelling of heavy tails, skewness, and extremes. While the primary focus is on statistical frameworks and theoretical advances, applications that demonstrate the practical impact—particularly in finance, climate science, health economics, actuarial science, and related areas—are strongly encouraged. We welcome articles on, but not limited to, the following themes: - Development of new univariate and multivariate distribution families - Extreme value modelling, including non-stationary and threshold-based EVT, generalized extreme value and Pareto models - Covariate-dependent tail index modelling and quantile-based frameworks - Skewed, heavy-tailed, and asymmetric distribution constructions - Copula-based dependence modelling, tail dependence analysis, and vine copulas for high-dimensional data - Neural density estimation, normalizing flows, and deep generative models with theoretical guarantees - Bayesian and penalized likelihood approaches for complex and misspecified models - Robust inference and diagnostics under heavy-tailed scenarios - Applications advancing understanding of extremes or dependence in finance, climate, epidemiology, actuarial science, and beyondAccepted article types include Original Research, Review, Mini Review, Hypothesis & Theory, Perspective, and Code & Data papers. Topic editors: Fastel Chipepa, Retius Chifurira, Daniel Maposa, Tendai Makoni Source: https://www.frontiersin.org/research-topics/79064/advances-in-distribution-theory-extreme-values-heavy-tailed-and-skewed-models-and-machine-learning-integration