Probability Distributions Involving Gaussian Random Variables

This handbook, now available in paperback, brings together a comprehensive collection of mathematical material in one location. It also offers a variety of new results interpreted in a form that is particularly useful to engineers, scientists, and applied mathematicians. The handbook is not specific to fixed research areas, but rather it has a generic flavor that can be applied by anyone working with probabilistic and stochastic analysis and modeling.

• Classic results are presented in their final form without derivation or discussion, allowing for much material to be condensed into one volume.
• Concise compilation of disparate formulae saves time in searching different sources.
• Focused application has broad interest for many disciplines: engineers, computer scientists, statisticians, physicists; as well as for any researcher working in probabilistic and stochastic analysis and modeling in the natural or social sciences.
• The material is timeless, with intrinsic value to practicing engineers and scientists.

Excerpts from reviews of the hardbound edition:

This is a unique book and an invaluable reference for engineers and scientists in the fields of electrical engineering, mathematics and statistics. There is no other single reference book that covers Gaussian and Gaussian-related distributions of random variables that are encountered in research work and practice. This is a reference book that I recommend to all my graduate students working in the area of telecommunication system analysis and design.

--John Proakis, Professor Emeritus, Northeastern University and Adjunct Professor, University of California, San Diego

The reference book Probability Distributions Involving Gaussian Random Variables, authored by Dr. Marvin Simon, has become, in a very short time frame, one of the most useful aids to research in the field of digital communications that has come out in many years. It has numerous results that can save researchers in the field endless hours of work. It has replaced various other well known resources because of its concentration of relevant, timely, and easily accessible results.

-- Larry Milstein, UCSD

There are a small number of reference works that have proven so invaluable that I have purchased a home copy in addition to my office copy. This handbook is one of them.

-- Dr. Norman C. Beaulieu, University of Alberta

The Gaussian distribution and those derived from it are at the very core of a huge number of problems in multi-disciplinary fields of engineering, mathematics and science... The book, with its comprehensive information in analytical, tabular, and graphical form, is an invaluable tool for scientists and engineers.

-- Sergio Benedetto, Politecnico di Torino

More testimonials can be found in the front of this edition.

Contenu

A Brief Biography of Carl Friedrich Gauss.- Preface.- Acknowledgment.- Introduction.- Basic Definitions and Notation.- Fundamental One-Dimensional Variables.- Fundamental Multidimensional Variables.- Difference of Chi-Square Random Variables.- Sum of Chi-Square Random Variables.- Products of Random Variables.- Ratios of Random Variables.- Maximum and Minimum of Pairs of Random Variables.- Quadratic Forms.- Other Miscellaneous Forms.- Appendix A: Alternative Forms.- One-Dimensional Distributions and Functions.- Two-Dimensional Distributions and Functions.- Appendix B: Integrals Involving Q-Functions.- The Gaussian Q-Function.- The First-Order Marcum Q-Function.- The Generalized (MTH-Order) Marcum Q-Function.- Appendix C: Bounds on the Gaussian Q-Function and the Marcum Q-Function.- The Gaussian Q-Function.- The Marcum Q-Function.- References.- Illustrations.