In the random walk whose state space is a subset of the non-negative integers explicit representations for the generating functions of the n-step transition and the first return probabilities are ...

This paper deals with the simple Galton-Watson process with immigration, {Xn} with offspring probability generating function (p.g.f.)F (s) and immigration p.g.f. B (s), under the basic assumption that ...

image: Examples of the possible multimodal shapes of the probability density function of a new modified normal distribution view more Credit: Christophe Chesneau/University of Caen-Normandie As is ...