Algorithms for generating random variables with a rational probability-generating function

Two algorithms for generating random variables with a rational probability-generating function are presented. One of them implements the recently developed general range reduction method, and the other is an extension of the alias method designed for generating discrete finite-valued random variables to the case where the generated random variable is infinite-valued. An example of a random variable which was efficiently generated by random number generators implementing the presented algorithms is given. Possible ways of improving the complexity of the presented algorithms are discussed.