The Inverse Gaussian Distribution : A Case Study in Exponential Families
by
V. Seshadri
Book Details
Format
Hardback or Cased Book
ISBN-10
0198522436
ISBN-13
9780198522430
Publisher
Oxford University Press
Imprint
Clarendon Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jan 20th, 1994
Print length
268 Pages
Weight
574 grams
Dimensions
24.20 x 16.20 x 2.00 cms
Product Classification:
Probability & statisticsStochastics
Ksh 35,700.00
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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.
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.
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