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.'
J.L. Folks, Oklahoma State University, International Statistical Institute, Vol. 14, No. 3 - December 1994
1: A historical survey
2: Properties of the inverse Gaussian distribution
5: Inverse natural exponential families on R
6: Statistical properties
Series: Oxford Science Publications
Number Of Pages: 272
Published: 20th January 1994
Country of Publication: GB
Dimensions (cm): 24.33 x 16.36
Weight (kg): 0.58