Επισκόπηση γενικών και ειδικών μεθόδων παραγωγής τυχαίων αριθμών από μονοδιάστατες και πολυδιάστατες κατανομές
Τζιώτης, Βασίλειος Α.
In this dissertation we initially conduct a review of the most well-known random number generation methods, such as the inversion method, the rejection-acceptance method and the composition method, for discrete and continuous distributions. Next we carry out a presentation of some special, lesser known but equally satisfactory methods for random number generation that can be used in cases where the previous methods are difficult to im¬plement. These special methods include the Forsythe-Von Neymann method, the "almost exact inversion" method, the "many to one transformation" method, the method of presenta¬tions of densities as integrals and the ratio of uniforms method. Finally, a brief reference is made regarding random number generation for some specific multivariate distributions, in¬cluding the Multivariate Normal Distribution and other related Distributions. In the process of presenting these techniques, an attempt was made in order to identify the most efficient algorithms for specific distributions and to compare their effectiveness. All corresponding algorithms were implemented using the software package "Wolfram Mathematica".