The Inverse Gaussian Distribution

A Case Study in Exponential Families

By: V. Seshadri

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Hardcover | 20 January 1994

At a Glance

Hardcover
272 Pages

Dimensions(cm)
23.39 x 15.6 x 1.6

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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 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.

Industry 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

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