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- Gaussian Scale MixturesPublication . Felgueiras, Miguel Martins; Martins, João Paulo; Santos, Rui Filipe; European Society of Computational Methods in Sciences and Engineering (ESCMSE)In this paper we present a parsimonious approximation of a Gaussian mixture when its components share a common mean value, i.e. a scale mixture. We show that a shifted and scaled Student’s t -distribution can be approximated to this type of mixture, and use the result to develop a hypothesis test for the equality of the components mean value. A simulation study to check the quality of the approximation is also provided, together with an application to logarithmic daily returns.