Recent Advances in Probability Distributions: Construction, Properties, and Applications

Probability distributions remain central to statistical modelling, inference, and decision-making across the mathematical, natural, medical, and engineering sciences. They provide the formal language for describing uncertainty, variability, and random behaviour, and they continue to play a key role in both methodological and applied research. While classical distributions remain fundamental, many contemporary data analysis problems require more flexible modelling tools with richer structural properties, improved interpretability, and stronger applicability to specialized settings such as lifetime analysis, reliability studies, biomedical outcomes, industrial processes, and count or bounded data.In recent years, substantial progress has been made in the development of new probability distribution families and in the study of their mathematical, inferential, and computational properties. These advances include new generator mechanisms, transformation-based constructions, extensions of classical models, and tractable formulations for data exhibiting non-standard support, censoring, truncation, or complex hazard behaviour. At the same time, there is growing interest in better understanding the theoretical properties of such models, including identifiability, stochastic ordering, entropy, moments, quantile structure, and estimation performance.This Research Topic aims to highlight recent progress in the construction, analysis, estimation, and application of probability distributions across a broad range of scientific domains. It seeks contributions that advance distribution theory in a rigorous and practically meaningful way, whether through the introduction of new models, the study of their properties, the development of estimation and diagnostic tools, or the demonstration of their usefulness in applied settings. The emphasis is on probability distributions as modelling tools in their own right, and on the mathematical and statistical insight they provide.We welcome submissions addressing, but not limited to, the following themes:1. Construction of New Distribution Families- Development of new continuous, discrete, and mixed probability distributions- Transformation-based constructions and generator methods- Extensions and generalizations of classical distributions- Composite, compounded, and hierarchical distribution families- Bounded-support, circular, directional, and count distributions2. Mathematical and Statistical Properties- Distributional properties, including moments, generating functions, and quantile functions- Entropy and information-based measures- Stochastic ordering, ageing properties, and shape characteristics- Characterizations of distributions- Identifiability, parameter interpretability, and structural properties3. Estimation, Inference, and Computation- Maximum likelihood, Bayesian, method-of-moments, and alternative estimation procedures- Computational methods for fitting complex distributions- Goodness-of-fit assessment and model comparison- Diagnostics, simulation studies, and performance evaluation- Inference under censoring, truncation, missingness, or grouped data4. Survival, Lifetime, and Reliability Modelling- Lifetime and failure-time distributions- Hazard rate modelling and ageing classes- Reliability analysis for engineering and industrial systems- Parametric and semi-parametric models for time-to-event data- Applications involving censored and truncated survival data5. Applied Distributional Modelling- Applications of probability distributions in medicine, public health, biology, engineering, economics, demography, and environmental studies- Distribution-based modelling for count, proportion, bounded, or circular data- Case studies demonstrating practical value of new or existing distributions- Comparative applied analyses showing when flexible distributions improve inference or predictionSubmissions may include theoretical, methodological, computational, or applied contributions, provided they offer clear advances in the understanding or use of probability distributions. Accepted article types include Original Research, Review, Mini Review, Hypothesis & Theory, Perspective, and Methods articles. Topic editors: Aliyu Ismail Ishaq, Ahmad Abubakar Suleiman Source: https://www.frontiersin.org/research-topics/79229/recent-advances-in-probability-distributions-construction-properties-and-applications