Level-Crossing Problems and Inverse Gaussian Distributions
Closed-Form Results and Approximations
- 434 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Level-Crossing Problems and Inverse Gaussian Distributions
Closed-Form Results and Approximations
About this book
Level-Crossing Problems and Inverse Gaussian Distributions: Closed-Form Results and Approximations focusses on the inverse Gaussian approximation for the distribution of the first level-crossing time in a shifted compound renewal process framework. This approximation, whose name was coined by the author, is a successful competitor of the normal (or Cramér's), diffusion, and Teugels' approximations, being a breakthrough in its conditions and accuracy.
Since such approximations underlie numerous applications in risk theory, queueing theory, reliability theory, and mathematical theory of dams and inventories, this book is of interest not only to professional mathematicians, but also to physicists, engineers and economists.
People from industry with a theoretical background in level-crossing problems, e.g., from the insurance industry, can also benefit from reading this book.
Features:
- Primarily aimed at researchers and postgraduates, but may be of interest to some professionals working in related fields, such as the insurance industry
- Suitable for advanced courses in Applied Probability and, as a supplementary reading, for basic courses in Applied Probability
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Information
Table of contents
- Cover
- Half Title
- Series Page
- Title Page
- Copyright Page
- Dedication
- Contents
- Preface
- 1 Introduction: level-crossing problem and related fields
- 2 Inverse Gaussian and generalized inverse Gaussian distributions
- 3 Integral expressions
- 4 Distribution of compound renewal process at a fixed time point
- 5 Closed-form results for the distribution of first level-crossing time
- 6 The inverse Gaussian approximation
- 7 Refinement of the inverse Gaussian approximation
- 8 Derivatives of the first level-crossing time distribution
- 9 A breakthrough in the level-crossing problem
- A Auxiliary results from analysis
- B Auxiliary results from probability
- List of notations
- Notes and comments
- Bibliography
- Index