New discrete Appell and Humbert distributions with relevance to bivariate accident data

The paper categorizes discrete multivariate distributions into classes according to the forms of their probability generating functions, putting especial emphasis on those with pgf’s involving Lauricella functions. The LPSDs are Lauricella power series distributions where the arguments of the function are proportional to the generating variables. Lauricella factorial moment distributions, LFMDs, have arguments of the form λ i ( s i − 1 ) , where s i is a generating variable. New LFMDs are created; the differences between these and Xekalaki’s generalized Waring distribution are clarified using bivariate accident models.