The inverse Gaussian distribution : a case study in exponential families / V. Seshadri.

Author
Seshadri, V. [Browse]
Format
Book
Language
English
Published/​Created
Oxford : Clarendon Press ; New York : Oxford University Press, ©1993.
Description
vii, 256 pages : illustrations ; 24 cm.

Availability

Copies in the Library

Location Call Number Status Location Service Notes
Lewis Library - Stacks QA276.7 .S47 1993 Browse related items Request

    Details

    Subject(s)
    Series
    Oxford science publications [More in this series]
    Summary note
    "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"--Publisher's description.
    Notes
    "Oxford science publications."--Cover.
    Bibliographic references
    Includes bibliographical references (p. [212]-243) and indexes.
    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.
    ISBN
    • 0198522436
    • 9780198522430
    LCCN
    93037707
    OCLC
    28890814
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