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Distribution mixture models are widely used in cluster analysis. Particularly, a mixture of Student t-distributions is mostly applied for robust data clustering. In this paper, we introduce EM algorithm for a mixture of Student distributions, where at the E-step, we apply variational Bayesian inference for parameters estimation. Based on a mixture of Student distributions, a machine learning method is constructed that allows solving regression problems for any set of features, clustering, and anomaly detection within one model. Each of these problems can be solved by the model even if there are missing values in the data. The proposed method was tested on real data describing the PVT properties of reservoir fluids. The results obtained by the model do not contradict the basic physical properties. In majority of conducted experiments our model gives more accurate results than well-known machine learning methods in terms of MAPE and RMSPE metrics.