Statistical Properties of the Generalized Inverse Gaussian Distribution

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Inhalt

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.