Finite mixtures have found application in various areas including meteorology. The purpose of this master’s thesis is to study finite mixtures with focus on parameter estimation in the concept of the EM algorithm. Overview of finite mixtures and EM algorithm estimators for the parameters of specific finite mixtures are given. In addition, finite mixtures are used to model Estonian meteorological data. Various finite mixtures are fitted on Estonian daily wind speed data and normal mixtures on daily temperature data.