The Laplace Distribution and Generalizations

1. Front Matter

   Pages i-xviii

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2. Univariate Distributions

   1. Front Matter

      Pages 1-1

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   2. Historical Background

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 3-13

   3. Classical Symmetric Laplace Distribution

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 15-131

   4. Asymmetric Laplace Distributions

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 133-178

   5. Related Distributions

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 179-225

3. Multivariate Distributions

   1. Front Matter

      Pages 227-227

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   2. Introduction

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 229-230

   3. Symmetric Multivariate Laplace Distribution

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 231-238

   4. Asymmetric Multivariate Laplace Distribution

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 239-272

4. Applications

   1. Front Matter

      Pages 273-273

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   2. Introduction

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 275-275

   3. Engineering Sciences

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 277-287

   4. Financial Data

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 289-302

   5. Inventory Management and Quality Control

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 303-308

   6. Astronomy and the Biological and Environmental Sciences

      • Samuel Kotz, Tomaz J. Kozubowski, Krzysztof Podgórski

      Pages 309-313

5. Back Matter

   Pages 315-349

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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).

• Distribution
• STATISTICA
• Stochastic Processes
• actuarial
• applied probability
• communication
• communications
• finance fields
• finance/economics
• modeling
• operations research
• statistics

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)

• Department of Engineering Management and Systems Engineering, George Washington University, Washington, USA

  Samuel Kotz

• Department of Mathematics, University of Nevada, Reno, USA

  Tomaz J. Kozubowski

• Department of Mathematical Sciences, Indiana University—Purdue University, Indianapolis, USA

  Krzysztof Podgórski

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