The Laplace distribution and generalizations. A revisit with applications to communications, economics, engineering, and finance. (English) Zbl 0977.62003

Boston: Birkhäuser. xviii, 349 p. (2001).
This book is devoted to presenting properties, generalizations and applications of the Laplace distribution (the first Laplace’s law of the error with the density: \((k/2)\exp (-k|x|))\). This distribution is a natural and sometimes superior alternative to the normal distribution (the second Laplace’s law of the error).
First, the univariate Laplace distribution is studied. The multivariate and skewed Laplace distributions are discussed in detailed form. The related distributions and stochastic processes to which they lead are objects of special chapters (Bessel function distribution; Laplace motion; Linnik distribution). Special chapters are devoted to applications in the engineering sciences (e.g., to the encoding and decoding of analog signals), in analysis of financial data (e.g., exchange rates, option pricing, etc.), in inventory management and quality control and to applications in astronomy, biological and environmental sciences. The rich set of exercises is an integral part of the discussion.


62-02 Research exposition (monographs, survey articles) pertaining to statistics
62Pxx Applications of statistics
62E15 Exact distribution theory in statistics
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
62E10 Characterization and structure theory of statistical distributions