Overview

In 1978 the idea of studying the generalized inverse Gaussian distribution was proposed to me by Professor Ole Barndorff-Nielsen, who had come across the distribution in the study of the socalled hyperbolic distributions where it emerged in connection with the representation of the hyperbolic distributions as mixtures of normal distributions. The statistical properties of the generalized inverse Gaussian distribution were at that time virtually unde- veloped, but it turned out that the distribution has some nice properties, and models many sets of data satisfactorily. This work contains an account of the statistical properties of the distribu- tion as far as they are developed at present. The work was done at the Department of Theoretical Statistics, Aarhus University, mostly in 1979, and was partial fulfilment to- wards my M.Sc. degree. I wish to convey my warm thanks to Ole Barn- dorff-Nielsen and Preben BI~sild for their advice and for comments on earlier versions of the manuscript and to Jette Hamborg for her skilful typing.

Full Product Details

Author:   B. Jorgensen ,  B Jorgensen
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1982
Volume:   9
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.314kg
ISBN:  

9780387906652

ISBN 10:   0387906657
Pages:   188
Publication Date:   16 December 1981
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1 Introduction.- 2 Basic properties.- 2.1 Moments and cumulants.- 3 Related distributions.- 3.1 Normal approximations.- 3.2 Powers and logarithms of generalized inverse Gaussian variates.- 3.3 Products and quotients of generalized inverse Gaussian variates.- 3.4 A generalized inverse Gaussian Markov process.- 3.5 The generalized hyperbolic distribution.- 4 Maximum likelihood estimation.- 4.1 Estimation for fixed ?.- 4.2 On the asymptotic distribution of the maximum likelihood estimate for fixed ?.- 4.3 The partially maximized log-likelihood for ?, estimation of ?.- 4.4 Estimation of ? when ? and ? are fixed.- 4.5 Estimation of ? when ? and ?>0 are fixed.- 5 Inference.- 5.1 Distribution results.- 5.2 Inference about ?.- 5.3 Inference about ?.- 5.4 One-way analysis of variance.- 5.5 A regression model.- 6 The hazard function. Lifetime models..- 6.1 Description of the hazard function.- 7 Examples.- 7.1 Failures of airconditioning equipment.- 7.2 Pulses along a nerve fibre.- 7.3 Traffic data.- 7.4 Repair time data.- 7.5 Fracture toughness of MIG welds.- References.- List of symbols.

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