Berger A., Hill T.P. An introduction to Benford’s law

USA, Princeton: Princeton University Press, 2017. — 397 p.This book is an up-to-date reference on Benford’s law, a statistical phenomenon first documented in the nineteenth century. Benford’s law, also known as the significant-digit law, is a subject of great beauty, encompassing counterintuitive predictions, deep mathematical theories, and widespread applications ranging from fraud detection to diagnosis and design of mathematical models. Building on over a decade of our joint work, this text is a self-contained comprehensive treatment of the theory of Benford’s law that includes formal deɹnitions and proofs, open problems, dozens of basic theorems we discovered in the process of writing that have not before appeared in print, and hundreds of examples. Complementing the theory are overviews of its history, new empirical evidence, and applications.