A mixed poisson–inverse‐gaussian regression model
- 1 June 1989
- journal article
- Published by Wiley in The Canadian Journal of Statistics / La Revue Canadienne de Statistique
- Vol. 17 (2) , 171-181
- https://doi.org/10.2307/3314846
Abstract
The mixed Poisson–inverse‐Gaussian distribution has been used by Holla, Sankaran, Sichel, and others in univariate problems involving counts. We propose a Poisson–inverse‐Gaussian regression model which can be used for regression analysis of counts. The model provides an attractive framework for incorporating random effects in Poisson regression models and in handling extra‐Poisson variation. Maximum‐likelihood and quasilikelihood‐moment estimation is investigated and illustrated with an example involving motor‐insurance claims.Keywords
This publication has 23 references indexed in Scilit:
- An extension of quasi-likelihood estimationJournal of Statistical Planning and Inference, 1989
- Tests for Detecting Overdispersion in Poisson Regression ModelsJournal of the American Statistical Association, 1989
- Parameter Orthogonality for a Family of Discrete DistributionsJournal of the American Statistical Association, 1988
- Parameter Orthogonality for a Family of Discrete DistributionsJournal of the American Statistical Association, 1988
- Linear models with an inverse gaussian poisson error distributionCommunications in Statistics - Theory and Methods, 1988
- On linear and quadratic estimating functionsBiometrika, 1987
- Parameter Estimation for the Sichel Distribution and its Multivariate ExtensionJournal of the American Statistical Association, 1987
- The poisson-inverse gaussian disiribuiion as a model for species abundanceCommunications in Statistics - Theory and Methods, 1986
- MODELS FOR RESPONSE DATA SHOWING EXTRA‐POISSON VARIATIONStatistica Neerlandica, 1984
- Statistical Properties of Inverse Gaussian Distributions. IThe Annals of Mathematical Statistics, 1957