Statistical Methods and Applications Using Quantiles

This book presents a unified and modern treatment of statistical methods based on quantiles, bridging classical regression, distributional modelling, and contemporary data analysis. Moving beyond mean-based approaches, it develops a coherent framework for modelling conditional and marginal distributions through quantile functions, with particular attention to interpretation, inference, and practical implementation. The book combines theoretical developments with applications across the health, social, environmental, and ecological sciences. Its aim is to provide both a conceptual foundation and a practical toolkit for researchers seeking robust, flexible, and interpretable methods for analysing complex data.

Key Features:

• A coherent treatment of statistical modelling through the lens of quantile functions
• Integration of conditional and unconditional quantiles within a single framework, bridging two strands of the literature that are typically treated separately
• Emphasis on distributional thinking, focusing on the entire outcome distribution rather than summary measures
• Coverage of advanced topics including mixed-effects and nonlinear quantile models
• Quantile-based tools for distributional comparison, including differences, ratios, and tail summaries
• Fully reproducible examples with R code using real and simulated datasets

The book is intended for graduate students, researchers, and practitioners in statistics, biostatistics, econometrics, and related fields. It is suitable for advanced courses on regression modelling, distributional methods, or applied data analysis, and can also serve as a reference for methodological research. Applied scientists working with heterogeneous or non-Gaussian data will find practical guidance for implementation and interpretation. A working knowledge of regression methods is assumed, while more advanced topics are developed progressively, allowing readers to engage with both foundational concepts and current research directions.

Marco Geraci is Professor of Statistics and Medical Statistics at Sapienza University of Rome and an internationally recognised expert in quantile-based statistical methods. His research focuses on the development of flexible modelling approaches for complex data, with applications in the health and social sciences. He has held academic positions at University College London, the University of Manchester, and the University of South Carolina. His work has been widely cited, with several publications recognised as highly cited contributions in statistics. Professor Geraci was Statistical Editor of the Journal of Child Health Care and has served on the editorial boards of leading statistical journals, including the Journal of the Royal Statistical Society Series A. He is a Fellow of the Royal Statistical Society and a member of the editorial board of Significance. He is also the author of widely used R packages for quantile modelling, which have contributed to the uptake of modern statistical methods in applied research.