A new bivariate negative binomial model for accident frequencies

The negative binomial model is widely used to describe the distribution of site accident frequencies. In studies of accident data over two time periods, or of two accident types, or in conflict analysis, it is useful to have a bivariate model. Senn and Collie recently proposed the use of a bivariate negative binomial model. Whilst this is appropriate for some applications, there are others for which it is too restrictive, in that the two true mean accident rates are taken to be perfectly correlated. This paper puts forward a new and more general bivariate negative binomial model and shows that the parameters can be estimated quite easily.