A common assumption in the majority of existing classification algorithms is that the stochastic distribution of the data being classified is stationary and does not change with time. However, in some real-word domains the data distribution can be non-stationary, implying that the distribution or characterizing aspects of the features change over time or the data generation phenomenon itself may change over time, which, in turn, leads to a variation in the data distribution. In this thesis, we consider a problem of C-class classification and of detecting the source of data in periodic non-stationary environments. Within our model, sequential patterns arrive and are processed in the form of a data stream that was generated from different sources with distinct statistical distributions. Using a family of Stochastic-Learning based Weak Estimators, we adopt a scheme to estimate the vector of the probability distribution of the binomial/multinomial datasets.