Canonical Expansion of the Compound Correlated Bivariate Poisson Distribution

Abstract

Edwards and Gurland [4] introduced the compound correlated bivariate Poisson (C.C.B.P.) distribution as a mathematical model applicable to bivariate accident data. It was shown that the marginal distributions of the C.C.B.P. were negative binomials. Moments were derived and regressions were proved to be linear. In the present article, the properties of the orthogonal polynomials with respect to the negative binomial distribution are used to derive the canonical expansion of the C.C.B.P. All properties of the bivariate distribution can be easily derived from its canonical form. As an application, we estimate the correlation coefficient for a contingency table with an underlying C.C.B.P. distribution.