Summary: A large portion of statistical literature pertains to the theory and application of nonparametric methods of inference. This work presents a new approach to some well-known statistical problems based on observation of a stochastic process. The recent development of the theory of probability allows us to consider these observations as ones of random variables with values in an infinite dimensional vector space. This paper will be devoted to estimation and testing by means of empirical generating functions \(G_n\). We use a similar procedure to that of Cramér-von Mises for various hypotheses testing problems.