In this work we study some probabilistic models for the random generation of words over a given alphabetused in the literature in connection with pattern statistics.Our goal is to compare models based on Markovian processes (where the occurrence of a symbol in a given positiononly depends on a finite number of previous occurrences) and the stochastic models that can generate a word of given length from a regular language under uniform distribution.We present some results that show the differences between these two stochastic models and theirrelationship with the rational probabilistic measures.