Considering that Y is generated through a Markov model of parameter π, the main goal of this paper is to study the distribution of SN, the statistic S computed using the estimators μN and πN, and the consequences of its variability in projects using pattern statistics. We first present in details how the delta-method can be used to get a Gaussian approximation for the distribution of SN (using a binomial approximation to compute the pattern statistics). Then these approximations are validated through simulations and, at last, we consider a classical pattern study (finding the most over-represented patterns of a given size) and we evaluate the detrimental effect of parameter estimations both in terms of true positive rate and rank accordance.