Statistical Properties of the Generalized Inverse Gaussian Distribution

Inhaltsverzeichnis

• 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.