The Inverse Gaussian Distribution A Case Study in Exponential Families [Hardcover]

This book provides a comprehensive and penetrating account of the inverse Gaussian law. Beginning with an exhaustive historical overview that presents--for the first time--Etienne Halphen's pioneering wartime contributions, the book proceeds to a rigorous exposition of the theory of exponential families, focusing in particular on the inverse Gaussian law. The book also considers inverse natural exponential families and provides a detailed analysis of the Tweedie scale. A wealth of properties, characterization, new concepts of inverse exponential families, useful expositions of statistical results, and an updated list of about 400 key references are included as well. The book will be welcomed by students and researchers of statistics and probability.

1. A historical survey
2. Properties of the inverse Gaussian distribution
3. Characterizations
4. Combinations
5. Inverse natural exponential families on R
6. Statistical properties
References
Author index
Subject index

This text provides a thorough, predominantly theoretical, overview of the inverse gaussian distribution and should prove indispensable to those who have discovered the value of this distribution in quality and reliability engineering applications. --Journal of Quality Technology