Stochastic Visibility in Random Fields

Name: Stochastic Visibility in Random Fields
Price: 1442 SEK
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AvShelemyahu Zacks

1994

Del i serien Lecture Notes in Statistics

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Beskrivning

Visibility problems are of interest in a wide variety of operations research and communications problems. This monograph presents an analysis of the "visibility" of one point in the plane from another given the existence of random objects which may obstruct the line of sight. The author aims to emphasize the practical issues involved, and describes the algorithms discussed. In addition, a DOS diskette containing executable programs which implement these algorithms is provided. The author presupposes a basic familiarity with probability, statistics and geometry, but otherwise the book is self-contained. As a result, researchers across a number of disciplines will find this account a useful introduction to the problem.

Produktinformation

Utgivningsdatum:1994-12-13
Höjd:155 x 235 x 11 mm
Vikt:306 g
Språk:Engelska
Serie:Lecture Notes in Statistics
Antal sidor:175
Upplaga:1994
Förlag:Springer-Verlag New York Inc.
EAN:9780387944128

Utforska kategorier

Innehållsförteckning

0. Introduction.- 0.1. Aims and Objectives.- 0.2. Some Military Applications.- 0.3. Synopsis.- 1. Probability Models.- 1.1. Probability Models For Obscuring Elements.- 1.2. Glossary of Distributions.- 1.3. Random Fields.- 2. Geometrical Probability, Coverage and Visibility in Random Fields.- 2.1. Intersection of Lines By Random Segments.- 2.2. Random Lines Intersecting Circles.- 2.3. Random Disks Intersecting Lines.- 2.4. The Coverage of a Circle By Random Arcs.- 2.5. Vacancies On The Circle.- 2.6. Vacancies On The Plane.- 2.7. Visitiblity of Points on a Circle In a Poisson Field.- 2.8. Distribution of Clump Size In a Poisson Field on The Line.- 3. Visibility Probabilities.- 3.1. Geometric Methods: Standard Poisson Fields.- 3.2. Analytic Methods: General Poisson Fields.- 3.3. An Alternative Geometric-Analytic Method.- 3.4. The Visibility of Windows.- 4. Visibility Probabilities II.- 4.1. The Multi-Observer Multi-Target Shadowing Model and Simultaneous Visibility Probabilities.- 4.2. General Formulae of mk(n,n?) for the Standard Poisson Field.- 4.3. Determination of mk(n,n?) in Cases of Non-Standard Poisson Fields.- 4.4. Joint Visibility of Windows.- 4.5. Visibility of Points in Space.- 5. Distributions of Visibility Measures.- 5.1. The Distribution of The Number of Visible Targets.- 5.2. An Integrated Measure of Visibility on a Star-Shaped Curve.- 5.3. The Moments of W.- 5.4. Approximations to the Distribution of W.- 6. Distributions of The Visible and Invisible Segments.- 6.1. The Distribution of The Length of A Visible Segment.- 6.2. The Functions K+*(x,t) in the Standard-Uniform Case.- 6.3. Distribution of The Right-Hand Limit of A Shadow Cast by a Single Disk.- 6.4. Distribution of The Right Hand Limit of a Shadow Starting at a Given Point.- 6.5. DiscreteApproximation.- 6.6. Distribution of the Number of Shadows.- 6.7. Survival Probability Functions.- 7. Problems and Solutions.- 7.1.1. Problems For Chapter 1.- 7.1.2. Solutions For Chapter 1.- 7.2.1. Problems For Chapter 2.- 7.2.2. Solutions For Chapter 2.- 7.3.1. Problems For Chapter 3.- 7.3.2. Solutions For Chapter 3.- 7.4.1. Problems For Chapter 4.- 7.4.2. Solutions For Chapter 4.- 7.5.1. Problems For Chapter 5.- 7.5.2. Solutions For Chapter 5.- 7.6.1. Problems For Chapter 6.- 7.6.2. Solutions For Chapter 6.- References.- Computer Programs.