Synopses & Reviews
This monograph focuses on the importance of the Laplace distribution and describes the inferential and modeling advantages that this distribution, together with its generalizations and modifications, offers. After presenting an historical introduction to the subject, the authors collect and present in a systematic way the univariate Laplace distribution, knowledge of which until now has been scattered in the vast statistical, engineering, and mathematical literature. The multivariate and skewed Laplace distribution are discussed here for the first time in detailed monograph form. Generalizations of Laplace distributions and stochastic processes to which they lead are presented as well. Many results, particularly those on the multivariate and skewed Laplace distribution, appear in print for the first time. The exposition systematically unfolds with many examples, tables, illustrations, and exercises. A comprehensive index and extensive bibliography also make this book an ideal text for a senior undergraduate and graduate seminar on statistical distributions, or for a short half-term academic course in statistics, applied probability, and finance. Key to the growing interest in the Laplace distribution are its applications, in particular, financial applications. The book covers interesting and recent applications of models based on the Laplace distribution, and will serve as a guide to development in this area of applied research for a broad audience of statisticians, finance experts, economists, engineers, and health scientists. Finally, in opening a new field of research in the theory of statistical distributions, The Laplace Distribution and Generalizations should strongly appeal to those working in theoretical or applied probability theory.
Review
From the reviews: "This book will be useful for those who are interested in tractable models which allow one to go beyond the normal distribution." (ISI SHORT BOOK REVIEWS) " A useful source of information for research in applied and theoretical statistics. No doubt, this volume will become a necessary part of any mathematical and statistical library as well as of a number of technical libraries."(MATHEMATICAL REVIEWS) "This book is devoted to presenting properties, generalizations and applications of the Laplace distribution ... This distribution is a natural and sometimes superior alternative to the normal distribution ... The rich set of exercises is an integral part of the discussion."(ZENTRALBLATT MATH)
Synopsis
An increasing number of researchers in various fields find the Laplace distribution an attractive and theoretically sound alternative to the normal and related distributions. This monograph describes the inferential and modeling advantages which the Laplace distribution offers and stresses the importance of its revival. Many new results are presented as well. Numerous examples, open problems, and exercises round out the presentation which will serve a broad audience interested in learning about the potential of this distribution.
Synopsis
The aim of this monograph is quite modest: It attempts to be a systematic exposition of all that appeared in the literature and was known to us by the end of the 20th century about the Laplace distribution and its numerous generalizations and extensions. We have tried to cover both theoretical developments and applications. There were two main reasons for writing this book. The first was our conviction that the areas and situations where the Laplace distribution naturally occurs is so extensive that tracking the original sources is unfeasible. The second was our observation of the growing demand for statistical distributions having properties tangent to those exhibited by the Laplace laws. These two "necessary" conditions justified our efforts that led to this book. Many details are arranged primarily for reference, such as inclusion of the most commonly used terminology and notation. In several cases, we have proposed unification to overcome the ambiguity of notions so often present in this area. Personal taste may have done some injustice to the subject matter by omitting or emphasizing certain topics due to space limitations. We trust that this feature does not constitute a serious drawback-in our literature search we tried to leave no stone unturned (we collected over 400 references).
Synopsis
This book describes the inferential and modeling advantages that this distribution, together with its generalizations and modifications, offers. The exposition systematically unfolds with many examples, tables, illustrations, and exercises. A comprehensive index and extensive bibliography also make this book an ideal text for a senior undergraduate and graduate seminar on statistical distributions, or for a short half-term academic course in statistics, applied probability, and finance.
Table of Contents
Preface * Part I. Univariate Distributions * 1. Historical Background * 2. Classical Symmetric Laplace Distribution * 3. Asymmetric Laplace Distributions * 4. Related Distributions * Part II. Multivariate Distributions * 5. Symmetric Multivariate Laplace Distribution * 6. Asymmetric Multivariate Laplace Distribution * Part III. Applications * 7. Engineering Sciences * 8. Financial Data * 9. Inventory Management and Quality Control * 10. Astronomy, Biological and Environmental Sciences * Appendix A. Bessel Functions * References * Index