A unified treatment is given for a class of discrete distributions der
ived by compounding a bivariate Poisson with a bivariate discrete or c
ontinuous distribution. Using generating functions a number of interes
ting results are obtained for probabilities, moments, cumulants, facto
rial moments, and factorial cumulants. Conditional distributions and r
egression functions are also examined. Five illustrative examples are
presented in detail. (C) 1994 John Wiley & Sons, Inc.