This book deals with estimating and testing the probability of an event. The purpose of the book is twofold: It aims at providing practitioners with refined and easy to use techniques as well as initiating a new field of research in theoretical statistics. The book contains completely new interval and point estimators that are superior to the traditional ones. This is especially true in the case of small and medium sized samples, which are characteristic for many fields of application. The estimators are tailored to a given situation and take into account the generally one knows the size of the probability to be measured. Thus, according the size of the probability different estimators should be used, similar to the case of measuring length, where the measurement method depends heavily on the size of the length to be measured. The approach yields more precise estimators and more powerful tests. It may also be applied to other estimation problems.

"The book addresses professional and academic statisticians, offering a non-standard look [at] statistics, tracing its roots and major developments, and deriving easy-to-apply methods. ...Different groups of readers are likely to benefits from this handbook.  For those interested in the theory, Part II explains its details. For readers only interested in the applications, Part II can be skipped without hampering the overall understanding of the approach. The book is easy to read, the language is clear and extensive. ...The theoretical details are given with mathematical rigour assuming a basic mathematical background from the reader. Erudite accounts of the historical aspects of stochastics and the enlightening debates on some controversial viewpoints add to the handbook's appeal."

--The Mathematical Gazette