The Inverse Gaussian Distribution: A Case Study in Exponential Families

Hardcover | January 1, 1992

byV. Seshadri

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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 specialcase. 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.

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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 functi...

V. Seshadri is at McGill University.

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Format:HardcoverDimensions:268 pages, 9.21 × 6.14 × 0.79 inPublished:January 1, 1992Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198522436

ISBN - 13:9780198522430

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Table of Contents

1. A historical survey2. Properties of the inverse Gaussian distribution3. Characterizations4. Combinations5. Inverse natural exponential families on R6. Statistical propertiesReferencesAuthor indexSubject index

Editorial Reviews

`This book is an important addition to the literature on the inverse Gaussian distribution.'J.L. Folks, Oklahoma State University, International Statistical Institute, Vol. 14, No. 3 - December 1994