Many people have helped and motivated me during the last three years in Florence. I think that acknowledgements to these people therefore represent the best starting point for my PhD thesis. Firstly, I really would like to thank my supervisor, Professor Giovanni Maria Marchetti, for his availability and his great support both in method-ological studies and in computational analysis. He introduced me graphical modelling research sharing his knowledge and also directing me towards stud-ies for discrete distributions. As regards models for discrete distributions, I would like to thank Wicher Bergsma. He gave me the opportunity to stay at the EURANDOM research centre in Eindhoven, Holland. In that period he encouraged me with interest-ing and s...