A Compendium of Univariate Statistical Distributions

Statistical distributions are the bedrock of statistical theory and practice, offering models that describe the behavior of data across countless domains, from engineering to economics, biology to social sciences. In particular, univariate statistical distributions, those that describe the distribution of a single variable, are of immense importance. They help statisticians model randomness, quantify uncertainty, and make inferences about populations from sample data. With this book, A Compendium of Univariate Statistical Distributions, we aim to provide a comprehensive, accessible, and systematic guide to the fundamental univariate distributions encountered in statistical analysis. The journey of this book begins with an exploration of a variety of univariate distributions, ranging from the widely known and studied distributions such as the Normal, Exponential, and Binomial, to the less commonly encountered yet equally important ones like the Birnbaum-Sanders, and von Mises distributions. Each chapter is dedicated to a particular distribution, providing the reader with a deep dive into its characteristics, and basic properties. Throughout this book, our goal has been not only to provide detailed theoretical insights but also to offer practical guidance on the use of each distribution in applied settings. We hope that readers will find this work not only informative but also inspiring, helping to deepen their understanding of the power and versatility of statistical distributions in the world of data analysis.