Probability Distributions Involving Gaussian Random Variables

A Handbook for Engineers and Scientists
2002. Auflage 2002
ISBN: 978-1-4020-7058-7
Verlag: Springer Us

Buch, Englisch, Band 683, 200 Seiten, Format (B × H): 179 mm x 228 mm, Gewicht: 513 g

Reihe: The Springer International Series in Engineering and Computer Science

This book is intended for use by students, academicians and practicing engineers who in the course of their daily study or research have need for the probability distributions and associated statistics of random variables that are themselves Gaussian or in various forms derived from them. The format of the book is primarily that of a handbook in that, for the most part, the results are merely presented in their final form without derivation or discussion. As such the reader must rely on the typographical accuracy of the documented expressions, which the author has taken great pains to assure. Also included at the end of the book are numerous curves illustrating the behavior of a variety of the probability measures presented in mathematical form. The author wishes to acknowledge his many colleagues in industry and academia for the encouragement and support they provided for this project without which it might never have gotten started. INTRODUCTION There are certain reference works that engineers and scientists alike find invaluable in their day-to-day work activities. Many of these reference volumes are of a generic nature such as tables of integrals, tables of series, handbooks of mathematical formulas and transforms, etc. (see Refs. 1, 2, 3, and 4 for example), whereas others are collections of technical papers and textbooks that directly relate to the individual's specific field of specialty.

Zielgruppe

Research

Autoren/Hrsg.

Simon, Marvin K

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Automatische Datenerfassung, Datenanalyse
• Technische Wissenschaften Technik Allgemein Modellierung & Simulation
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.