Generalized Markov-Polya urn models with predetermined strategies

By using combinatorial methods involving lattice path combinatorics, three generalized probability models dependent on predetermined strategies have been obtained with the help of urn models. The models have been developed with the help of a sampling scheme which unifies both, the binomial and the inverse binomial sampling schemes. These models generate a number of important discrete probability distributions both as particular cases and as limiting cases. Recurrence relations among the moments of the models have also been obtained.