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The inverse Gaussian distribution : a case study in exponential families

Author: V Seshadri
Publisher: Oxford : Clarendon Press ; New York : Oxford University Press, ©1993.
Series: Oxford science publications.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"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  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: V Seshadri
ISBN: 0198522436 9780198522430
OCLC Number: 28890814
Description: vii, 256 pages : illustrations ; 24 cm.
Contents: l. A historical survey --
1.0 Introduction and motivation --
1.1 Bachelier's derivation --
1.2 Schrödinger's derivation --
1.3 Smoluchowski's derivation --
1.4 Tweedie's rationale --
1.5 Wald's derivation --
1.6 Huff's derivation --
1.7 A heuristic derivation --
1.8 Martingale methods --
1.9 Halphen's laws --
2 Properties of the inverse Gaussian distribution --
2.0 Introduction --
2.1 Natural exponential families --
2.2 The inverse Gaussian law and natural exponential families --
2.3 General exponential families --
2.4 Analogies with the Gaussian law --
2.5 Reproductive exponential families --
2.6 Saddle-point approximation and the inverse Gaussian law --
2.7 Barndorff-Nielsen's p* formula and the inverse Gaussian law --
2.8 Miscellaneous results --
2.9 The distribution function --
2.10 Notes and additional comments --
3 Characterizations --
3.0 Introduction --
3.1 Characterizations analogous to the Gaussian law --
3.2 Characterization by constant regression --
3.3 Characterization by random continued fractions --
3.4 Characterization by relation between E(x⁻¹) and E(X) for exponential family on R+ --
4 Combinations, extensions, and relatives --
4.0 Introduction --
4.1 A class of finite mixtures --
4.2 Multivariate distributions --
4.3 Combinations-models generated by IG/RJG laws --
4.4 Kolmogorov-Smirnov statistics and the inverse Gaussian law --
4.5 Miscellaneous results --
4.6 Notes and additional comments --
5 Inverse natural exponential families on R --
5.0 Introduction --
5.1 The class M and inversion in M --
5.2 Inverse pair of natural exponential families on R --
5.3 Convolutions of positive measures --
5.4 Mora-Morris classification of cubic exponential families --
5.5 Infinite divisibility --
5.6 The Tweedie scale --
5.7 Lévy processes on the real line --
5.8 Right continuous random walks and inversion --
6 Statistical properties --
6.0 Introduction --
6.1 Estimation --
6.2 Tests of hypotheses --
6.3 Generalized linear models and the inverse Gaussian law --
6.4 Regression methods --
6.5 Bayesian inference --
6.6 Simulation of inverse Gaussian variates.
Series Title: Oxford science publications.
Responsibility: V. Seshadri.
More information:

Abstract:

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,  Read more...

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Publisher Synopsis

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 Read more...

 
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