Probability Distributions Involving Gaussian Random Variables: A Handbook for Engineers and Scientists

Author:   Marvin K. Simon
Publisher:   Springer-Verlag New York Inc.
Edition:   1st ed. 2002. 2nd printing 2006
ISBN:  

9780387346571


Pages:   200
Publication Date:   09 November 2006
Format:   Paperback
Availability:   In Print   Availability explained
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Probability Distributions Involving Gaussian Random Variables: A Handbook for Engineers and Scientists


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Full Product Details

Author:   Marvin K. Simon
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1st ed. 2002. 2nd printing 2006
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   0.730kg
ISBN:  

9780387346571


ISBN 10:   0387346570
Pages:   200
Publication Date:   09 November 2006
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

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.

Reviews

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. <p> <ul> <p> <li>Classic results are presented in their final form without derivation or discussion, allowing for much material to be condensed into one volume.</li> <p> <li>Concise compilation of disparate formulae saves time in searching different sources</li> <p> <li>Focused application has broad interest for many disciplines: engineers, computer scientists, statisticians, physicists; as well as any researcher working in probabilistic and stochastic analysis and modeling in the natural or social sciences.</li> <p> <li>The material is timeless and has intrinsic value to todaya (TM)s and tomorrowa (TM)s practicing engineers and scientists</li> <p> <li>Endorsed by top experts in field worldwide, ensuring quality and value</li> <p>Excerpts from reviews of the hardbound edition: <p>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 replaced various other well known resources because of its concentration of relevant, timely, and easily accessible results. a Dr. Larry Milstein, UCSD <p>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. a Dr. John Proakis, Northeastern University and UCSD <p>a ] this book collected all these results (after double-checking them) with unified notations and in an organized fashion made it very useful for many of the graduate students and researchers doing analytical type of investigations. Not only did I use it, I also recommend it to my graduate students and many of our papers benefited from the formulas available in the handbooka ]. The handbook saves valuable time for all the researchers that rely on it to simplify their results or write them in terms of well-known functions that are available in popular mathematical packages such as Matlab and Mathematica. a Dr. Mohamed-Slim Alouini, Texas A&M University <p>The distributions and associated statistics described in the book apply to systems like mobile and cellular communications, vehicular technology, radar systems, spread spectrum systems, and optical communication systems. The book, with its comprehensive information in analytical, tabular, and graphical form, is an invaluable tool for scientists and engineers. a Dr. Sergio Benedetto, Politecnico di Torino <p>The book Probability Distributions Involving Gaussian Random Variables is a handy research reference in areassuch as communication systems. I have found the book useful for my own work, since it presents probability distributions that are difficult to find elsewhere and that have non-obvious derivations. a Dr. Gordon StA1/4ber, Georgia Institute of Technology <p>A unique and invaluable reference for researchers in communications, signal processing, math, statistics, and many other scientific fields. I have used this book in my own research and also recommended it to colleagues in universities and in industry, as well as to graduate students. a Dr. Andrea Goldsmith, Stanford University <p>In my research in wireless communications, I have often found that I can get all the mathematical forms and material that I need from one source, where before I had to consult five or six references to get the complete information. There are a small number of reference works that have proved so invaluable that I have purchased a home copy in addition to my office copy. This handbook is one of them. a Dr. Norman C. Beaulieu, University of Alberta <p>Our research Group at the University of Canterbury is engaged in both theoretical and experimental work on advanced wireless communications systems. We have found that the book by Simon, Probability Distributions Involving Gaussian Random Variables is an indispensable and often used reference for this work. We do significant amounts of analysis involving Gaussian statistics and quadratic forms. The book is the one source that brings almost all of the necessary background material together in a readily usable form and is thus an extremely valuable reference. a Dr. Desmond P. Taylor, University of Canterbury <p>Dr. Simon's book is by far the mostcomprehensive compilation of Gaussian probability distributions and their associated statistics - in fact to my knowledge this is the only book of its type in publication now. This handbook is a much needed and most welcome entry to the toolbox of any engineer or scientist. For those working in digital and wireless communications, signal and image processing, pattern recognition, and many other technical fields, the text is absolutely essential. a Payman Arabshahi, Applied Physics Laboratory <p>As a researcher and teacher in the digital communication theory area for the last forty years, I can state that Simona (TM)s book contains materials in his ten chapters and appendices most relevant to researchers and developers of modern communication systems. These sophisticated Gaussian related expressions are needed in the analysis, design, and optimization of modern microwave and cellular communications. Many of these results are unavailable elsewhere, since these results were originated by Simon himself. a Dr. Kung Yao, UCLA <p>After I spent a few minutes trying to come up with my own derivation, I decided to consult Probability Distributions Involving Gaussian Random Variables, where I found the needed result within a few seconds. On this and many other occasions, I have found Marvin Simon's book to be a unique and extremely valuable resource for my own research. The book is even more crucial for the graduate students who, unlike those in my generation, did not grow up with the Gaussian Q function, Marcum's Q-function, Rayleigh and Rician distributions, chi-squared random variables, and all the other important functions, distributions, and concepts that have their roots in Gaussian random variables. a Dr. Michael B. Pursley, Clemson University <p>Because the source of randomness and noise is usually modeled as Gaussian, engineers and scientists often need the probability distributions of functions of Gaussian random variables. Marvin Simon has written an extremely useful handbook for everyone working in these fields. It is by far the most complete and easy-to-use collection of these characterizations of functions of Gaussian random variables. a ]an important and very popular book that is useful to a very large community of engineers and scientists. This work is also very carefully done with many corrections to earlier works that were not easily available to this community. a Jim Omura, Technology Strategist, Gordon and Betty Moore Foundation <p>The handbook Probability Distributions Involving Gaussian Random Variables by Marvin K. Simon is a wonderful resource for both theoreticians and practitioners in that it contains a wealth of information summarized in one book. a Dr. Costas N. Georghiades, Texas A&M University <p>From the reviews: <p> This handbook for engineers, scientists and mathematicians a ] is a collection of results intended for use by graduate students, practicing engineers and scientists who need probability distributions involving normal or Gaussian random variables. a ] Results on differences, sums, products, ratios, maximum and minimum of random variables, as well as a brief biography of Carl Friedrich Gauss are also included. (Andreas N. Philippou, Zentralblatt MATH, Vol. 1121 (23), 2007)


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 any researcher working in probabilistic and stochastic analysis and modeling in the natural or social sciences. * The material is timeless and has intrinsic value to today's and tomorrow's practicing engineers and scientists * Endorsed by top experts in field worldwide, ensuring quality and value Excerpts from reviews of the hardbound edition: 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 replaced various other well known resources because of its concentration of relevant, timely, and easily accessible results. -Dr. Larry Milstein, UCSD 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. -Dr. John Proakis, Northeastern University and UCSD ... this book collected all these results (after double-checking them) with unified notations and in an organized fashion made it very useful for many of the graduate students and researchers doing analytical type of investigations. Not only did I use it, I also recommend it to my graduate students and many of our papers benefited from the formulas available in the handbook... The handbook saves valuable time for all the researchers that rely on it to simplify their results or write them in terms of well-known functions that are available in popular mathematical packages such as Matlab and Mathematica. -Dr. Mohamed-Slim Alouini, Texas A&M University The distributions and associated statistics described in the book apply to systems like mobile and cellular communications, vehicular technology, radar systems, spread spectrum systems, and optical communication systems. The book, with its comprehensive information in analytical, tabular, and graphical form, is an invaluable tool for scientists and engineers. -Dr. Sergio Benedetto, Politecnico di Torino The book Probability Distributions Involving Gaussian Random Variables is a handy research reference in areas such as communication systems. I have found the book useful for my own work, since it presents probability distributions that are difficult to find elsewhere and that have non-obvious derivations. -Dr. Gordon Stuber, Georgia Institute of Technology A unique and invaluable reference for researchers in communications, signal processing, math, statistics, and many other scientific fields. I have used this book in my own research and also recommended it to colleagues in universities and in industry, as well as to graduate students. -Dr. Andrea Goldsmith, Stanford University In my research in wireless communications, I have often found that I can get all the mathematical forms and material that I need from one source, where before I had to consult five or six references to get the complete information. There are a small number of reference works that have proved 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 Our research Group at the University of Canterbury is engaged in both theoretical and experimental work on advanced wireless communications systems. We have found that the book by Simon, Probability Distributions Involving Gaussian Random Variables is an indispensable and often used reference for this work. We do significant amounts of analysis involving Gaussian statistics and quadratic forms. The book is the one source that brings almost all of the necessary background material together in a readily usable form and is thus an extremely valuable reference. -Dr. Desmond P. Taylor, University of Canterbury Dr. Simon's book is by far the most comprehensive compilation of Gaussian probability distributions and their associated statistics - in fact to my knowledge this is the only book of its type in publication now. This handbook is a much needed and most welcome entry to the toolbox of any engineer or scientist. For those working in digital and wireless communications, signal and image processing, pattern recognition, and many other technical fields, the text is absolutely essential. -Payman Arabshahi, Applied Physics Laboratory As a researcher and teacher in the digital communication theory area for the last forty years, I can state that Simon's book contains materials in his ten chapters and appendices most relevant to researchers and developers of modern communication systems. These sophisticated Gaussian related expressions are needed in the analysis, design, and optimization of modern microwave and cellular communications. Many of these results are unavailable elsewhere, since these results were originated by Simon himself. -Dr. Kung Yao, UCLA After I spent a few minutes trying to come up with my own derivation, I decided to consult Probability Distributions Involving Gaussian Random Variables, where I found the needed result within a few seconds. On this and many other occasions, I have found Marvin Simon's book to be a unique and extremely valuable resource for my own research. The book is even more crucial for the graduate students who, unlike those in my generation, did not grow up with the Gaussian Q function, Marcum's Q-function, Rayleigh and Rician distributions, chi-squared random variables, and all the other important functions, distributions, and concepts that have their roots in Gaussian random variables. -Dr. Michael B. Pursley, Clemson University Because the source of randomness and noise is usually modeled as Gaussian, engineers and scientists often need the probability distributions of functions of Gaussian random variables. Marvin Simon has written an extremely useful handbook for everyone working in these fields. It is by far the most complete and easy-to-use collection of these characterizations of functions of Gaussian random variables. ...an important and very popular book that is useful to a very large community of engineers and scientists. This work is also very carefully done with many corrections to earlier works that were not easily available to this community. -Jim Omura, Technology Strategist, Gordon and Betty Moore Foundation The handbook Probability Distributions Involving Gaussian Random Variables by Marvin K. Simon is a wonderful resource for both theoreticians and practitioners in that it contains a wealth of information summarized in one book. -Dr. Costas N. Georghiades, Texas A&M University


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