Positive-Unlabeled learning (PU learning) is a binary classification task where only a subset of positive instances are labeled. The objective is then to find the correct classifier using positive labeled instances and unlabeled instances that contain a mixture of positive and negative data. In this paper, we illustrate some recent results about the convergence rates of PU learning under the general Selected At Random assumption, meaning that the labeled instances are not assumed to be a representative sample of the positive instances. We show that the simulations support the theoretical results highlighting the two regimes of convergence. We finally extend the simulations by relaxing some assumptions.