This paper presents an extension of the mathematical model used to justify accident proneness. It assumes that the distribution of accidents incurred by an individual in non-overlapping intervals is a correlated bivariate Poisson (C.B.P.). On compounding this correlated bivariate Poisson through a Gamma distribution an extended bivariate negative binomial or, more precisely, a compound correlated bivariate Poisson (C.C.B.P.) distribution is obtained. Recurrence relations and expressions for the required probabilities are illustrated for two sets of data. The C.C.B.P. proved to fit as well as the bivariate negative binomial when the estimate of B12was close to zero, and much better than the latter distribution when the estimate of B12 was not close to zero.