Ebook: The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance
- Tags: Statistical Theory and Methods, Applications of Mathematics, Statistics for Business/Economics/Mathematical Finance/Insurance
- Year: 2001
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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).
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 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.
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 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.
Content:
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Historical Background....Pages 3-13
Classical Symmetric Laplace Distribution....Pages 15-131
Asymmetric Laplace Distributions....Pages 133-178
Related Distributions....Pages 179-225
Front Matter....Pages 227-227
Introduction....Pages 229-230
Symmetric Multivariate Laplace Distribution....Pages 231-238
Asymmetric Multivariate Laplace Distribution....Pages 239-272
Front Matter....Pages 273-273
Introduction....Pages 275-275
Engineering Sciences....Pages 277-287
Financial Data....Pages 289-302
Inventory Management and Quality Control....Pages 303-308
Astronomy and the Biological and Environmental Sciences....Pages 309-313
Back Matter....Pages 315-349
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 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.
Content:
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
Historical Background....Pages 3-13
Classical Symmetric Laplace Distribution....Pages 15-131
Asymmetric Laplace Distributions....Pages 133-178
Related Distributions....Pages 179-225
Front Matter....Pages 227-227
Introduction....Pages 229-230
Symmetric Multivariate Laplace Distribution....Pages 231-238
Asymmetric Multivariate Laplace Distribution....Pages 239-272
Front Matter....Pages 273-273
Introduction....Pages 275-275
Engineering Sciences....Pages 277-287
Financial Data....Pages 289-302
Inventory Management and Quality Control....Pages 303-308
Astronomy and the Biological and Environmental Sciences....Pages 309-313
Back Matter....Pages 315-349
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