The Inverse Gaussian Distribution
A Case Study in Exponential Families
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80 141 Ft
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Product details:
- Publisher Clarendon Press
- Date of Publication 20 January 1994
- Number of Volumes laminated boards
- ISBN 9780198522430
- Binding Hardback
- No. of pages268 pages
- Size 242x162x20 mm
- Weight 574 g
- Language English
- Illustrations line figures 0
Categories
Short description:
Beginning with a historical survey, the book provides a comprehensive overview of natural exponential families, with emphasis on the inverse Gaussian Law. Included are a range of properties, characterizations, new concepts of inverse exponential families, useful expositions of statistical results, and an updated list of approximately 400 references.
MoreLong description:
This book begins with a historical survey of `generalized inverse Gaussian laws', in which the wartime contribution of Etienne Halphen is presented for the first time.
The inverse Gaussian distribution, its properties, and its implications are set in a wide perspective. The concepts of inversion and inverse natural exponential functions are presented, together with an analysis of the `Tweedie' scale, of which the Gaussian distribution is an important special case.
Chapter 2 concerns the basic theory of exponential functions, focusing on the inverse Gaussian Law. Chapter 3 is devoted to various characterization results, while Chapter 4 is concerned with the construction of multivariate distributions, and the relationship to simplex distributions, combinations, and finite mixtures. Chapter 5 introduces the concept of inverse natural exponential functions and Chapter 6 presents useful statistical results.
Up-to-date research is presented in the form of exercises, a special chapter on characterizations is included, and a summary of statistical issues concerning estimation and interference are provided. Research workers will find inspiration for further investigations.
This book is an important addition to the literature on the inverse Gaussian distribution.
Table of Contents:
A historical survey
Properties of the inverse Gaussian distribution
Characterizations
Combinations
Inverse natural exponential families on R
Statistical properties
References
Author index
Subject index
